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A111723 Number of partitions of an n-set with an odd number of blocks of size 1. 9
1, 0, 4, 4, 31, 86, 449, 1968, 10420, 56582, 333235, 2069772, 13606113, 94065232, 682242552, 5175100432, 40954340995, 337362555010, 2886922399649, 25616738519384, 235313456176512, 2234350827008170, 21899832049913999, 221292603495494488, 2302631998398438321 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..576

FORMULA

E.g.f.: sinh(x)*exp(exp(x)-1-x).

More generally, e.g.f. for number of partitions of an n-set with an odd number of blocks of size k is sinh(x^k/k!)*exp(exp(x)-1-x^k/k!).

MAPLE

b:= proc(n, t) option remember; `if`(n=0, t, add(b(n-j,

      `if`(j=1, 1-t, t))*binomial(n-1, j-1), j=1..n))

    end:

a:= n-> b(n, 0):

seq(a(n), n=1..30);  # Alois P. Heinz, May 10 2016

MATHEMATICA

Rest[ Range[0, 23]! CoefficientList[ Series[ Sinh[x]Exp[Exp[x] - 1 - x], {x, 0, 23}], x]] (* Robert G. Wilson v *)

PROG

(Python)

from sympy.core.cache import cacheit

from sympy import binomial

@cacheit

def b(n, t):

    return t if n==0 else sum(b(n - j, (1 - t if j==1 else t))*binomial(n - 1, j - 1) for j in range(1, n + 1))

def a(n):

    return b(n, 0)

print([a(n) for n in range(1, 51)]) # Indranil Ghosh, Aug 10 2017

CROSSREFS

Cf. A097514, A113235, A063083, A062282, A111724, A111752, A111753.

Sequence in context: A065237 A264586 A307499 * A337447 A239601 A196131

Adjacent sequences:  A111720 A111721 A111722 * A111724 A111725 A111726

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Nov 17 2005

EXTENSIONS

More terms from Robert G. Wilson v, Nov 22 2005

STATUS

approved

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Last modified April 14 16:31 EDT 2021. Contains 342949 sequences. (Running on oeis4.)