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 A305842 Product_{n>=1} (1 + x^n)^a(n) = g.f. of A000293 (solid partitions). 0

%I

%S 1,4,6,14,15,26,26,48,46,83,97,146,112,49,-186,-448,-735,-485,779,

%T 3977,9323,16569,23056,23996,10116,-31501,-120720,-283153,-548924,

%U -932348,-1380125,-1655520,-1144651,1384894,7943203,21083482,42787785,71816970,98995196

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

%C Inverse weigh transform of A000293.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SolidPartition.html">Solid Partition</a>

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

%e (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 + ...

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

%K sign

%O 1,2

%A _Ilya Gutkovskiy_, Jun 11 2018

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Last modified April 8 21:44 EDT 2020. Contains 333329 sequences. (Running on oeis4.)