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A235596 Second column of triangle in A235595. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 map(a, range(1, 31)) # Indranil Ghosh, Aug 26 2017

CROSSREFS

Cf. A000248, A235595.

Sequence in context: A231134 A038112 A268039 * A052512 A166554 A038156

Adjacent sequences:  A235593 A235594 A235595 * A235597 A235598 A235599

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 15 2014

STATUS

approved

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Last modified January 26 16:58 EST 2020. Contains 331280 sequences. (Running on oeis4.)