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A257674
INVERT transform of planar partitions.
4
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 03 2015
STATUS
approved