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A111724 Number of partitions of an n-set with an even number of blocks of size 1. 9
0, 2, 1, 11, 21, 117, 428, 2172, 10727, 59393, 345335, 2143825, 14038324, 96834090, 700715993, 5305041715, 41910528809, 344714251149, 2945819805408, 26107419715988, 239556359980239, 2272364911439153, 22252173805170347, 224666265799310801, 2335958333831561032 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

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

More generally, e.g.f. for number of partitions of an n-set with an even number of blocks of size k is cosh(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, 1):

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

MATHEMATICA

Rest[ Range[0, 24]! CoefficientList[ Series[ Cosh[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, 1)

print map(a, range(1, 51)) # Indranil Ghosh, Aug 10 2017

CROSSREFS

Cf. A097514, A113235, A063083, A062282, A111723, A111752, A111753.

Sequence in context: A300455 A270264 A305877 * A184299 A080371 A151337

Adjacent sequences:  A111721 A111722 A111723 * A111725 A111726 A111727

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 9 14:25 EDT 2020. Contains 333355 sequences. (Running on oeis4.)