A393222 Column 2 of A372254.

1, 18, 426, 15402, 822954, 61796298, 6241779786, 818474614122, 135406656802794, 27612620496455178, 6808731437920094346, 1997715795041570812842, 688004411488219400750634, 274892797454182595423594058, 126140171858432431734157512906, 65889765750203313093270839555562

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

a(n) ~ 8 * sqrt(Pi) * n^(2*n+5/2) / (sqrt(1 - log(2)) * exp(2*n) * log(2)^(2*n+3)).

Mathematica

g[n_] := g[n] = If[n == 0, 1, Sum[Expand[x*g[n-j]]*Binomial[n-1, j-1], {j, 1, n}]]; A[n_, k_] := A[n, k] = Module[{q, l, b}, {q, l} = {-1, {n, n, k}}; b[n0_, j_] := b[n0, j] = If[j == 1, Product[q-i, {i, 0, n0-1}]*(q-n0)^l[[1]], Sum[b[n0 + m, j-1]*Coefficient[g[l[[j]]], x, m], {m, 0, l[[j]]}]]; Abs[b[0, 3]]]; Table[A[n, 2], {n, 0, 20}] (* after Jean-François Alcover *)

Crossrefs

Cf. A372254.

Sequence in context: A172135 A005477 A361549 * A326368 A197343 A289941

Adjacent sequences: A393219 A393220 A393221 * A393223 A393224 A393225

Keyword

nonn

Author

Vaclav Kotesovec, Feb 06 2026

Status

approved