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A130223 Number of partitions of n-set in which number of blocks of size 2k-1 is odd (or zero) for every k. 5
1, 1, 1, 5, 8, 42, 117, 541, 2403, 10485, 65778, 282262, 2284493, 9977853, 97315935, 450358629, 4966934284, 25167390922, 298399576813, 1693380647429, 20784317362947, 134137856170593, 1658511579778364, 12262539123056548, 150144857708406161, 1273792249691584593 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

FORMULA

E.g.f.: exp(cosh(x)-1)*Product_{k>0} (1+sinh(x^(2*k-1)/(2*k-1)!)).

MAPLE

with(combinat):

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(

      `if`(j=0 or irem(i, 2)=0 or irem(j, 2)=1, multinomial(

       n, n-i*j, i$j)/j!*b(n-i*j, i-1), 0), j=0..n/i)))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..30);  # Alois P. Heinz, Mar 08 2015

MATHEMATICA

max = 26; f[x_] = Exp[Cosh[x]-1]*Product[1+Sinh[x^(2*k-1)/(2*k-1)!], {k, 0, max}]; CoefficientList[f[x] + O[x]^max, x]*Range[0, max-1]! (* Jean-Fran├žois Alcover, Jul 01 2015 *)

CROSSREFS

Cf. A102759.

Sequence in context: A258786 A192272 A073930 * A126750 A256401 A109292

Adjacent sequences:  A130220 A130221 A130222 * A130224 A130225 A130226

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Aug 05 2007, Aug 05 2007

EXTENSIONS

More terms from Max Alekseyev, Jan 31 2010

STATUS

approved

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Last modified June 1 09:53 EDT 2020. Contains 334762 sequences. (Running on oeis4.)