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, 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

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