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

0,3

Links

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

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

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 *)

Crossrefs

Row sums of A257673.

Cf. A000219.

Sequence in context: A219708 A345230 A117882 * A027123 A291236 A339850

Adjacent sequences: A257671 A257672 A257673 * A257675 A257676 A257677

Keyword

nonn

Author

Alois P. Heinz, May 03 2015

Status

approved