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A257674 INVERT transform of planar partitions.

%I A257674 #23 Aug 22 2021 14:10:20
%S A257674 1,1,4,13,44,144,478,1573,5193,17118,56457,186153,613865,2024192,
%T A257674 6674843,22010313,72579382,239331323,789198395,2602391853,8581422014,
%U A257674 28297352194,93310894654,307693910316,1014624748161,3345738548716,11032617200372,36380201398917
%N A257674 INVERT transform of planar partitions.
%H A257674 Alois P. Heinz, <a href="/A257674/b257674.txt">Table of n, a(n) for n = 0..1930</a>
%F A257674 a(n) = Sum_{k=0..n} A257673(n,k).
%F A257674 a(n) ~ c * d^n, where d = 3.2975132503126723336836261261699651439543806296893328114462016186843..., c = 0.3713883419445088444000361183895708557141471246022776707501762842135... . - _Vaclav Kotesovec_, May 19 2015
%F A257674 G.f.: 1/(2 - Product_{k>=1} 1/(1 - x^k)^k). - _Ilya Gutkovskiy_, Oct 18 2018
%p A257674 g:= proc(n) option remember; `if`(n=0, 1, add(
%p A257674       g(n-j)*numtheory[sigma][2](j), j=1..n)/n)
%p A257674     end:
%p A257674 a:= proc(n) option remember; `if`(n=0, 1,
%p A257674       add(a(n-i)*g(i), i=1..n))
%p A257674     end:
%p A257674 seq(a(n), n=0..36);
%t A257674 g[n_] := g[n] = If[n==0, 1, Sum[g[n-j] DivisorSigma[2, j], {j, 1, n}]/n];
%t A257674 a[n_] := a[n] = If[n==0, 1, Sum[a[n-i] g[i], {i, 1, n}]];
%t A257674 Table[a[n], {n, 0, 36}] (* _Jean-François Alcover_, Aug 22 2021, after _Alois P. Heinz_ *)
%Y A257674 Row sums of A257673.
%Y A257674 Cf. A000219.
%K A257674 nonn
%O A257674 0,3
%A A257674 _Alois P. Heinz_, May 03 2015