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%I #9 Oct 25 2015 10:58:10
%S 1,1,2,5,12,37,143,562,2320,10941,54865,283890,1604155,9558226,
%T 58668223,384572975,2631778832,18576630237,137919691717,1060303298138,
%U 8415786131309,69538205444478,591734670548037,5194542789203877,47127033586211659,438972204436025198
%N Number of partitions of {1,...,n} into blocks such that no even sized block is repeated.
%H Alois P. Heinz, <a href="/A115277/b115277.txt">Table of n, a(n) for n = 0..500</a>
%F E.g.f.: exp(sinh(x)) * Product {m >= 1} (1+x^(2*m)/(2*m)!).
%p with(combinat):
%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1), j=0..min(
%p `if`(irem(i, 2)=0, 1, n), n/i))))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Mar 08 2015
%t multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j! * b[n-i*j, i-1], {j, 0, Min[If[Mod[i, 2]==0, 1, n], n/i]}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Oct 25 2015, after _Alois P. Heinz_ *)
%Y Cf. A001935, A115275, A115276, A115278.
%K nonn
%O 0,3
%A _Christian G. Bower_, Jan 18 2006
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