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.
%I A381345 #11 Feb 21 2025 05:52:14
%S A381345 1,1,2,0,-24,-220,-1200,-2576,52864,1016208,10909440,57039488,
%T A381345 -687971328,-26190716864,-450123634688,-4238375059200,24514848522240,
%U A381345 2156422420074752,54984136073084928,799573460292407296,42320889956270080,-425007017470737816576,-15563879892284330213376
%N A381345 Expansion of e.g.f. 1/( 1 - x * cos(sqrt(2)*x) ).
%C A381345 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381345 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-2)^k * (2*k+1) * binomial(n,2*k+1) * a(n-2*k-1).
%F A381345 a(n) = Sum_{k=0..n} k! * (-2)^((n-k)/2) * A185951(n,k).
%o A381345 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381345 a(n) = sum(k=0, n, k!*(-2)^((n-k)/2)*a185951(n, k));
%Y A381345 Cf. A205571, A352252, A381280, A381281, A381282, A381283, A381344.
%Y A381345 Cf. A185951.
%K A381345 sign
%O A381345 0,3
%A A381345 _Seiichi Manyama_, Feb 20 2025