A257674 INVERT transform of planar partitions.

1, 1, 4, 13, 44, 144, 478, 1573, 5193, 17118, 56457, 186153, 613865, 2024192, 6674843, 22010313, 72579382, 239331323, 789198395, 2602391853, 8581422014, 28297352194, 93310894654, 307693910316, 1014624748161, 3345738548716, 11032617200372, 36380201398917

Offset: 0

Author

Alois P. Heinz, May 03 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1930

Crossrefs

Row sums of A257673.

Cf. A000219.

Programs

Maple

g:= proc(n) option remember; `if`(n=0, 1, add(
      g(n-j)*numtheory[sigma][2](j), j=1..n)/n)
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(a(n-i)*g(i), i=1..n))
    end:
seq(a(n), n=0..36);

Mathematica

g[n_] := g[n] = If[n==0, 1, Sum[g[n-j] DivisorSigma[2, j], {j, 1, n}]/n];
a[n_] := a[n] = If[n==0, 1, Sum[a[n-i] g[i], {i, 1, n}]];
Table[a[n], {n, 0, 36}] (* Jean-François Alcover, Aug 22 2021, after Alois P. Heinz *)

Formula

a(n) = Sum_{k=0..n} A257673(n,k).

a(n) ~ c * d^n, where d = 3.2975132503126723336836261261699651439543806296893328114462016186843..., c = 0.3713883419445088444000361183895708557141471246022776707501762842135... . - Vaclav Kotesovec, May 19 2015

G.f.: 1/(2 - Product_{k>=1} 1/(1 - x^k)^k). - Ilya Gutkovskiy, Oct 18 2018