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A102760 Number of partitions of n-set into "lists", in which every even list appears an even number of times, cf. A000262. 2
1, 1, 1, 7, 37, 241, 1381, 13231, 140617, 1483777, 16211881, 217551511, 3384215341, 50221272817, 782154787597, 13913712591871, 272739557719441, 5282625708305281, 106588332600443857, 2354480141600267047, 56238135934525073461, 1338131691952924913521 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..445

FORMULA

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

MAPLE

with(combinat):

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

      add(`if`(i::even and j::odd, 0, b(n-i*j, i-1)*

      multinomial(n, n-i*j, i$j)/j!*i!^j), j=0..n/i)))

    end:

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

seq(a(n), n=0..25);  # Alois P. Heinz, May 10 2016

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[If[EvenQ[i] && OddQ[j], 0, b[n-i*j, i- 1] * multinomial[n, Join[{n - i*j}, Array[i &, j]]]/j!*i!^j], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 25}] (* Jean-Fran├žois Alcover, Feb 05 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A003483, A006950, A052565, A088026.

Sequence in context: A025012 A039938 A285846 * A096965 A159597 A217723

Adjacent sequences:  A102757 A102758 A102759 * A102761 A102762 A102763

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Feb 10 2005

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, May 10 2016

STATUS

approved

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Last modified June 26 00:41 EDT 2019. Contains 324367 sequences. (Running on oeis4.)