A293860 a(0) = 0, a(1) = 1; a(n) = n! * [x^n] exp(n*x)*Sum_{k=1..n-1} a(k)*x^k/k!.

0, 1, 4, 63, 1648, 65075, 3629196, 272106555, 26418426560, 3225539263995, 483800514119500, 87459323696213843, 18755503692216214320, 4707783117485450859987, 1367396879443428912151724, 455052324991418691450493275, 172012620929344322616321833728

Offset: 0

Author

Ilya Gutkovskiy, Oct 17 2017

Keywords

• nonn

Examples

			E.g.f. A(x) = x + 4*x^2/2! + 63*x^3/3! + 1648*x^4/4! + 65075*x^5/5! + 3629196*x^6/6! + ...
		

Crossrefs

Cf. A000629, A000670, A052882.

Programs

Mathematica

a[n_] := a[n] = n! SeriesCoefficient[Exp[n x] Sum[a[k] x^k/k!, {k, 1, n - 1}], {x, 0, n}]; a[0] = 0; a[1] = 1; Table[a[n], {n, 0, 16}]

Formula

a(n) ~ c * n^(2*n + 1 + log(2)/2) / (log(2)^n * exp(2*n)), where c = 2.715081809041541547553157767788588016035268429424586978200936... - Vaclav Kotesovec, Oct 18 2017