cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A102760 Number of partitions of n-set into "lists", in which every even list appears an even number of times, cf. A000262.

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