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 A381342 #11 Feb 21 2025 05:50:26
%S A381342 1,1,1,-5,-23,-39,361,2675,3697,-90575,-741839,52779,48483865,
%T A381342 358510985,-1225182503,-43006420829,-239523048095,2745896185953,
%U A381342 54532102774753,144304368441179,-6547928921714999,-88336890555248327,199686588300036553,18186115601328322515
%N A381342 Expansion of e.g.f. exp( x * cos(sqrt(2)*x) ).
%C A381342 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381342 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-2)^k * (2*k+1) * binomial(n-1,2*k) * a(n-2*k-1).
%F A381342 a(n) = Sum_{k=0..n} (-2)^((n-k)/2) * A185951(n,k).
%o A381342 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381342 a(n) = sum(k=0, n, (-2)^((n-k)/2)*a185951(n, k));
%Y A381342 Cf. A003727, A009189, A381273, A381274, A381275, A381276, A381341.
%Y A381342 Cf. A185951.
%K A381342 sign
%O A381342 0,4
%A A381342 _Seiichi Manyama_, Feb 20 2025