A193718 -id:A193718 - cp's OEIS frontend

A037452 Let F(x) = 1 + 1x + 4x^2 + 10*x^3 + ..., the g.f. for A000293 (solid partitions), and write F(x) = 1/Product_{n>=1} (1 - x^n)^a(n).

0, 1, 3, 6, 10, 15, 20, 26, 34, 46, 68, 97, 120, 112, 23, -186, -496, -735, -531, 779, 3894, 9323, 16472, 23056, 23850, 10116, -31613, -120720, -283202, -548924, -932162, -1380125, -1655072, -1144651, 1385629, 7943203, 21083967, 42787785, 71816191, 98995196, 100392874, 29623771, -187433150

Offset: 0

N. J. A. Sloane, May 02 2003

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Suresh Govindarajan, Table of n, a(n) for n = 0..72
Suresh Govindarajan, Exact Enumeration of Solid Partitions, IIT Madras.
D. E. Knuth, A Note on Solid Partitions, Math. Comp. 24, 955-961, 1970.

Cf. A000293, A002835, A080207, A193718.

More terms from Vladeta Jovovic, Jul 30 2003

A305842 Product_{n>=1} (1 + x^n)^a(n) = g.f. of A000293 (solid partitions).

Original entry on oeis.org

1, 4, 6, 14, 15, 26, 26, 48, 46, 83, 97, 146, 112, 49, -186, -448, -735, -485, 779, 3977, 9323, 16569, 23056, 23996, 10116, -31501, -120720, -283153, -548924, -932348, -1380125, -1655520, -1144651, 1384894, 7943203, 21083482, 42787785, 71816970, 98995196

Offset: 1

Ilya Gutkovskiy, Jun 11 2018

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Inverse weigh transform of A000293.

			(1 + x) * (1 + x^2)^4 * (1 + x^3)^6 * (1 + x^4)^14 * (1 + x^5)^15 * ... * (1 + x^n)^a(n) * ... = 1 + x + 4*x^2 + 10*x^3 + 26*x^4 + 59*x^5 + ... + A000293(k)*x^k + ...

N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Solid Partition

Cf. A000293, A001511, A037452, A193718, A305841.

Product_{n>=1} (1 + x^n)^a(n) = Sum_{k>=0} A000293(k)*x^k.

cp's OEIS Frontend

A037452 Let F(x) = 1 + 1x + 4x^2 + 10*x^3 + ..., the g.f. for A000293 (solid partitions), and write F(x) = 1/Product_{n>=1} (1 - x^n)^a(n).

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A305842 Product_{n>=1} (1 + x^n)^a(n) = g.f. of A000293 (solid partitions).

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cp's OEIS Frontend

A037452 Let F(x) = 1 + 1*x + 4*x^2 + 10*x^3 + ..., the g.f. for A000293 (solid partitions), and write F(x) = 1/Product_{n>=1} (1 - x^n)^a(n).

Views

Author

Keywords

Links

Crossrefs

Extensions

A305842 Product_{n>=1} (1 + x^n)^a(n) = g.f. of A000293 (solid partitions).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A037452 Let F(x) = 1 + 1x + 4x^2 + 10*x^3 + ..., the g.f. for A000293 (solid partitions), and write F(x) = 1/Product_{n>=1} (1 - x^n)^a(n).