%I #12 Feb 05 2017 07:51:29
%S 1,1,1,7,37,241,1381,13231,140617,1483777,16211881,217551511,
%T 3384215341,50221272817,782154787597,13913712591871,272739557719441,
%U 5282625708305281,106588332600443857,2354480141600267047,56238135934525073461,1338131691952924913521
%N Number of partitions of n-set into "lists", in which every even list appears an even number of times, cf. A000262.
%H Alois P. Heinz, <a href="/A102760/b102760.txt">Table of n, a(n) for n = 0..445</a>
%F E.g.f.: exp(x/(1-x^2))*Product_{k>0} cosh(x^(2*k)).
%p with(combinat):
%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p add(`if`(i::even and j::odd, 0, b(n-i*j, i-1)*
%p multinomial(n, n-i*j, i$j)/j!*i!^j), j=0..n/i)))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..25); # _Alois P. Heinz_, May 10 2016
%t 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-François Alcover_, Feb 05 2017, after _Alois P. Heinz_ *)
%Y Cf. A003483, A006950, A052565, A088026.
%K nonn
%O 0,4
%A _Vladeta Jovovic_, Feb 10 2005
%E a(0)=1 prepended by _Alois P. Heinz_, May 10 2016
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