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

1,3

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000248, A235595.

Sequence in context: A038112 A268039 A367044 * A346577 A367242 A052512

Adjacent sequences: A235593 A235594 A235595 * A235597 A235598 A235599

Keyword

nonn

Author

N. J. A. Sloane, Jan 15 2014

Status

approved