A393221 Column 1 of A372254.

1, 6, 78, 1902, 76110, 4553166, 381523758, 42700751022, 6157828055310, 1112444773251726, 246141320428525038, 65480501041227557742, 20623423521606515356110, 7590312777562545300695886, 3228104419544512535098911918, 1571129867418152272451563414062, 867697466760475249585357617786510

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) ~ 4 * sqrt(Pi) * n^(2*n+1) * n^(1/2) / (sqrt(1 - log(2)) * exp(2*n) * log(2)^(2*n+2)).

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, 1], {n, 0, 20}] (* after Jean-François Alcover *)

Crossrefs

Cf. A372254.

Sequence in context: A177556 A219435 A219135 * A208308 A353411 A053771

Adjacent sequences: A393218 A393219 A393220 * A393222 A393223 A393224

Keyword

nonn

Author

Vaclav Kotesovec, Feb 06 2026

Status

approved