A393221 - OEIS

%I #7 Feb 06 2026 09:04:49

%S 1,6,78,1902,76110,4553166,381523758,42700751022,6157828055310,

%T 1112444773251726,246141320428525038,65480501041227557742,

%U 20623423521606515356110,7590312777562545300695886,3228104419544512535098911918,1571129867418152272451563414062,867697466760475249585357617786510

%N Column 1 of A372254.

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

%t 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_ *)

%Y Cf. A372254.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Feb 06 2026