The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A096806

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A096806

Triangle, read by rows, such that the binomial transform of the n-th row lists the m-dimensional partitions of n, for n>=1 and m>=0.
(history; published version)

#12 by Jon E. Schoenfield at Fri Mar 13 19:13:05 EDT 2015

STATUS

editing

approved

#11 by Jon E. Schoenfield at Fri Mar 13 19:13:00 EDT 2015

EXAMPLE

The number of m-dimensional partitions of 5, for m>=0, is given by the binomial transform of the 5-th 5th row:

STATUS

approved

editing

#10 by Joerg Arndt at Fri Jun 29 14:38:20 EDT 2012

STATUS

proposed

approved

#9 by R. J. Mathar at Fri Jun 29 14:21:11 EDT 2012

STATUS

editing

proposed

#8 by R. J. Mathar at Fri Jun 29 14:20:43 EDT 2012

COMMENTS

The n-th row equals the inverse binomial transform of n-th column of square array A096751, for n>=1. The zero-dimensional partition of n is taken to be 1 for all n. The row sums form A096807.

LINKS

S. Govindarajan, <a href="http://arxiv.org/abs/1203.4419">Notes on higher-dimensional partitions</a>, arXiv:1203.4419

FORMULA

T(n, 0)=T(n, n-1)=1, T(n, 1)=A000041(n)-1, T(n+1, , n-12)=(n-1)*(n-2)/2+1, for n>=1.

EXAMPLE

BINOMIAL([1,6,11,7,1]) = [1,7,24,59,120,216,357,554,819,1165,...] = A008779.

CROSSREFS

Cf. A096751, A096807. (row sums), A000065 (column k=1?), A008778 (bin trans 4th row), A042984 (bin trans 6th row)

STATUS

approved

editing

#7 by Russ Cox at Fri Mar 30 18:36:41 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Jul 19 2004

Discussion

Fri Mar 30

18:36

OEIS Server: https://oeis.org/edit/global/213

#6 by N. J. A. Sloane at Sun Dec 09 03:00:00 EST 2007

COMMENTS

The n-th row equals the inverse Binomial binomial transform of n-th column of square array A096751, for n>=1. The zero-dimensional partition of n is taken to be 1 for all n. The row sums form A096807.

KEYWORD

nonn,tabl,new

#5 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

KEYWORD

nonn,tabl,new

AUTHOR

Paul D . Hanna (pauldhanna(AT)juno.com), Jul 19 2004

#4 by N. J. A. Sloane at Fri Sep 29 03:00:00 EDT 2006

CROSSREFS

Cf . A119271.

KEYWORD

nonn,tabl,new

#3 by N. J. A. Sloane at Fri May 19 03:00:00 EDT 2006

CROSSREFS

Cf A119271.

KEYWORD

nonn,tabl,new