The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A107268

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A107268

Sums of antidiagonals of A107267.
(history; published version)

#8 by Jon E. Schoenfield at Fri Dec 02 22:10:42 EST 2016

STATUS

editing

approved

#7 by Jon E. Schoenfield at Fri Dec 02 22:10:40 EST 2016

NAME

Sums of anti-diagonals antidiagonals of A107267.

STATUS

approved

editing

#6 by Alois P. Heinz at Sun Apr 13 12:31:16 EDT 2014

STATUS

editing

approved

#5 by Alois P. Heinz at Sun Apr 13 12:31:05 EDT 2014

LINKS

Alois P. Heinz, <a href="/A107268/b107268.txt">Table of n, a(n) for n = 0..250</a>

#4 by Alois P. Heinz at Sun Apr 13 12:29:40 EDT 2014

FORMULA

a(n) =sum Sum_{k=0..n, sum} Sum_{j=0..n-k, (} 1/(j+1)) C(j+1, n-k-j+1) C(n-k, j)k^j}}; a(n)=sum{k=0..n, sum{j=0..k, (1/(j+1))C(j+1, k-j+1)C(k, j)(n- k)^j}}.

a(n) = Sum_{k=0..n} Sum_{j=0..k} 1/(j+1) C(j+1,k-j+1) C(k,j) (n-k)^j.

STATUS

approved

editing

#3 by Russ Cox at Fri Mar 30 18:59:07 EDT 2012

AUTHOR

_Paul Barry (pbarry(AT)wit.ie), _, May 15 2005

Discussion

Fri Mar 30

18:59

OEIS Server: https://oeis.org/edit/global/287

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

FORMULA

a(n)=sum{k=0..n, sum{j=0..n-k, (1/(j+1))C(j+1, n-k-j+1)C(n-k, j)k^j}}; a(n)=sum{k=0..n, sum{j=0..k, (1/(j+1))C(j+1, k-j+1)C(k, j)(n-k)^j}}.

KEYWORD

easy,nonn,new

#1 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

NAME

Sums of anti-diagonals of A107267.

DATA

1, 1, 2, 5, 14, 46, 173, 733, 3436, 17572, 96997, 573268, 3604687, 23990345, 168254444, 1238889493, 9546211068, 76761000444, 642524333589, 5586361188966, 50351455288661, 469653513479395, 4526242614854118, 45005754238016688

OFFSET

0,3

FORMULA

a(n)=sum{k=0..n, sum{j=0..n-k,(1/(j+1))C(j+1,n-k-j+1)C(n-k,j)k^j}}; a(n)=sum{k=0..n, sum{j=0..k, (1/(j+1))C(j+1,k-j+1)C(k,j)(n-k)^j}}.

KEYWORD

easy,nonn

AUTHOR

Paul Barry (pbarry(AT)wit.ie), May 15 2005

STATUS

approved