A235596 Second column of triangle in A235595.

0, 0, 2, 9, 40, 195, 1056, 6321, 41392, 293607, 2237920, 18210093, 157329096, 1436630091, 13810863808, 139305550065, 1469959371232, 16184586405327, 185504221191744, 2208841954063317, 27272621155678840, 348586218389733555, 4605223387997411872, 62797451641106266329, 882730631284319415504

Offset: 1

Author

N. J. A. Sloane, Jan 15 2014

Keywords

• nonn

Examples

			G.f. = 2*x^3 + 9*x^4 + 40*x^5 + 195*x^6 + 1056*x^7 + 6321*x^8 + 41392*x^9 + ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000248, A235595.

Programs

Mathematica

gf[k_] := gf[k] = If[k == 0, x, x*E^gf[k-1]]; a[n_, k_] := n!*Coefficient[Series[gf[k], {x, 0, n+1}], x, n]; a[n_] := (a[n, 2] - a[n, 1])/n; Array[a, 25] (* Jean-François Alcover, Mar 18 2014, after Alois P. Heinz *)
Table[Sum[BellY[n - 1, k, Range[n - 1]], {k, 0, n - 2}], {n, 1, 25}] (* Vladimir Reshetnikov, Nov 09 2016 *)

Python

from sympy import binomial
from sympy.core.cache import cacheit
@cacheit
def b(n, h): return 1 if min(n, h)==0 else sum([binomial(n - 1, j - 1)*j*b(j - 1, h - 1)*b(n - j, h) for j in range(1, n + 1)])
def a(n): return b(n - 1, 1) - b(n - 1, 0)
print([a(n) for n in range(1, 31)]) # Indranil Ghosh, Aug 26 2017

Formula

a(n) = A000248(n-1) - 1. - Alois P. Heinz, Jun 21 2019