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.

A096939 Number of sets of odd number of even lists, cf. A000262.

This page as a plain text file.
%I A096939 #17 Dec 01 2021 10:48:47
%S A096939 0,2,6,36,260,1950,19362,193256,2326536,29272410,413257790,6231230412,
%T A096939 101415565836,1769925341366,32734873484250,646218442877520,
%U A096939 13404753632014352,294656673023216946,6775966692145553526
%N A096939 Number of sets of odd number of even lists, cf. A000262.
%H A096939 Vincenzo Librandi, <a href="/A096939/b096939.txt">Table of n, a(n) for n = 1..200</a>
%F A096939 E.g.f.: exp(x/(1-x^2))*sinh(x^2/(1-x^2)).
%F A096939 Recurrence: (n-2)*a(n) = (2*n-3)*a(n-1) + (n-1)*(2*n^2 - 8*n + 7)*a(n-2) + (n-2)*(n-1)*(2*n-5)*a(n-3) - (n-4)*(n-3)*(n-2)^2*(n-1)*a(n-4). - _Vaclav Kotesovec_, Sep 29 2013
%F A096939 a(n) ~ exp(2*sqrt(n)-n-1/2)*n^(n-1/4)/(2*sqrt(2)) * (1-5/(48*sqrt(n))). - _Vaclav Kotesovec_, Sep 29 2013
%F A096939 a(n) = A000262(n) - A096965(n). - _Alois P. Heinz_, Dec 01 2021
%t A096939 Drop[ Range[0, 20]! CoefficientList[ Series[ Exp[(x/(1 - x^2))] Sinh[x^2/(1 - x^2)], {x, 0, 20}], x], 1] (* _Robert G. Wilson v_, Aug 19 2004 *)
%Y A096939 Cf. A000262, A088026, A088009, A096965.
%K A096939 easy,nonn
%O A096939 1,2
%A A096939 _Vladeta Jovovic_, Aug 18 2004
%E A096939 More terms from _Robert G. Wilson v_, Aug 19 2004