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A132993 Triangle t(n,m) = P(n-m+1) * P(m+1) read by rows, 0<=m<=n, where P=A000041 are the partition numbers. 1
1, 2, 2, 3, 4, 3, 5, 6, 6, 5, 7, 10, 9, 10, 7, 11, 14, 15, 15, 14, 11, 15, 22, 21, 25, 21, 22, 15, 22, 30, 33, 35, 35, 33, 30, 22, 30, 44, 45, 55, 49, 55, 45, 44, 30, 42, 60, 66, 75, 77, 77, 75, 66, 60, 42, 56, 84, 90, 110, 105, 121, 105, 110, 90, 84, 56 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

1;

2, 2;

3, 4, 3;

5, 6, 6, 5;

7, 10, 9, 10, 7;

11, 14, 15, 15, 14, 11;

15, 22, 21, 25, 21, 22, 15;

22, 30, 33, 35, 35, 33, 30, 22;

30, 44, 45, 55, 49, 55, 45, 44, 30;

42, 60, 66, 75, 77, 77, 75, 66, 60, 42;

56, 84, 90, 110, 105, 121, 105, 110, 90, 84, 56;

MAPLE

A132993 := proc(n, m)

        combinat[numbpart](n-m+1)*combinat[numbpart](m+1) ;

end proc:

seq(seq(A132993(n, k), k=0..n), n=0..12) ; # R. J. Mathar, Nov 11 2011

MATHEMATICA

<< DiscreteMath`Combinatorica`; << DiscreteMath`IntegerPartitions`; Clear[t, n, m]; t[n_, m_] = PartitionsP[n - m + 1]*PartitionsP[m + 1]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

CROSSREFS

Cf. A000041, A048574 (row sums).

Sequence in context: A165634 A128282 A146985 * A106408 A143061 A096858

Adjacent sequences:  A132990 A132991 A132992 * A132994 A132995 A132996

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Aug 27 2008

STATUS

approved

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Last modified May 14 06:35 EDT 2021. Contains 343879 sequences. (Running on oeis4.)