The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A075798

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A075798

Triangle T(n,k) = f(n,k,n-1), n >= 0, 0 <= k <= n, where f is given below.
(history; published version)

#10 by Ralf Stephan at Fri Jan 17 05:38:48 EST 2014

STATUS

reviewed

approved

#9 by Joerg Arndt at Fri Jan 17 05:23:50 EST 2014

STATUS

proposed

reviewed

#8 by Jean-François Alcover at Fri Jan 17 04:52:13 EST 2014

STATUS

editing

proposed

#7 by Jean-François Alcover at Fri Jan 17 04:52:05 EST 2014

MATHEMATICA

f[n_, p_, k_] := Binomial[n, k]*HypergeometricPFQ[{1 - k, -p, p-n}, {1-n, 1}, 1]; t[n_, n_] = t[_, 0] = 1; t[n_, k_] := f[n, k, n-1]; Table[t[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 17 2014 *)

STATUS

approved

editing

#6 by Russ Cox at Fri Mar 30 16:49:31 EDT 2012

AUTHOR

_N. J. A. Sloane (njas(AT)research.att.com), _, Oct 17 2002

Discussion

Fri Mar 30

16:49

OEIS Server: https://oeis.org/edit/global/110

#5 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

KEYWORD

nonn,tabl,new

AUTHOR

N. J. A. Sloane (njas, (AT)research.att.com), Oct 17 2002

#4 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

CROSSREFS

Cf. A014410 and A007318 for f(n, k, n), A075779 and A075798 for f(n, k, n-1) and A075780 and A075837 for f(n, k, n-2).

KEYWORD

nonn,tabl,new

#3 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

f(n, p, k) = binomial(n, k)*hypergeom([1-k, -p, p-n], [1-n, 1], 1).

CROSSREFS

Cf. A014410 and A007318 for f(n,k,n), A075779 and A075798 for f(n,k,n-1), and A075780 and A075837 for f(n,k,n-2).

KEYWORD

nonn,tabl,new

#2 by N. J. A. Sloane at Sat Jun 12 03:00:00 EDT 2004

MAPLE

f := proc(n, p, k) convert( binomial(n, k)*hypergeom([1-k, -p, p-n], [1-n, 1], 1), `StandardFunctions`); end;

CROSSREFS

Cf. A014410 and A007318 for f(n,k,n); , A075779 and A075798 for f(n,k,n-1); , and A075780 and A075837 for f(n,k,n-2).

KEYWORD

nonn,tabl,new

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

Triangle T(n,k) = f(n,k,n-1), n >= 0, 0 <= k <= n, where f is given below.

DATA

1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 16, 12, 1, 1, 20, 35, 35, 20, 1, 1, 30, 66, 84, 66, 30, 1, 1, 42, 112, 175, 175, 112, 42, 1, 1, 56, 176, 328, 400, 328, 176, 56, 1, 1, 72, 261, 567, 819, 819, 567, 261, 72, 1, 1, 90, 370, 920, 1540, 1820, 1540, 920, 370, 90, 1, 1, 110, 506, 1419, 2706, 3696, 3696, 2706, 1419, 506, 110, 1, 1, 132, 672

OFFSET

1,5

LINKS

Michel Lassalle, <a href="http://arXiv.org/abs/math.CO/0210208">A new family of positive integers</a>

FORMULA

f(n,p,k) = binomial(n,k)*hypergeom([1-k,-p,p-n],[1-n,1],1).

EXAMPLE

1; 1,1; 1,2,1; 1,6,6,1; ...

MAPLE

f:=proc(n, p, k) convert( binomial(n, k)*hypergeom([1-k, -p, p-n], [1-n, 1], 1), `StandardFunctions`); end;

CROSSREFS

Cf. A014410 and A007318 for f(n,k,n); A075779 and A075798 for f(n,k,n-1); and A075780 and A075837 for f(n,k,n-2).

KEYWORD

nonn,tabl

AUTHOR

njas, Oct 17 2002

STATUS

approved