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

Author

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

Keywords

• nonn
• tabl

Examples

			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;
		

Crossrefs

Cf. A000041, A048574 (row sums).

Programs

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[%]