A385585 G.f. A(x) satisfies A(x) = Sum_{k>=0} (k*x)^k * A(k*x).

1, 1, 5, 40, 457, 7101, 148270, 4206121, 165267951, 9117777074, 709325010385, 77906424970811, 12109278363587036, 2670187179684919761, 836451775445907622685, 372646977140600929476104, 236390047765997660237447061, 213719117789650238860723125601

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} (n-k)^n * a(k).

From Vaclav Kotesovec, Jul 04 2025: (Start)

a(n) ~ c * 3^(n*(n+3)/6), where

c = 14331.87392277329... if mod(n,3) = 0,

c = 14331.87383811849... if mod(n,3) = 1,

c = 14331.87405112061... if mod(n,3) = 2. (End)

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[(n-k)^n * a[k], {k, 0, n-1}]; Table[a[n], {n, 0, 20}] (* Vaclav Kotesovec, Jul 04 2025 *)

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (i-j)^i*v[j+1])); v;

Crossrefs

Cf. A125282, A385544.

Cf. A218683.

Sequence in context: A052868 A292405 A094574 * A090362 A201366 A392966

Adjacent sequences: A385582 A385583 A385584 * A385586 A385587 A385588

Keyword

nonn

Author

Seiichi Manyama, Jul 03 2025

Status

approved