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 A381347 #10 Feb 21 2025 05:53:48
%S A381347 1,1,2,4,8,4,-112,-1184,-9088,-59504,-310528,-643136,14701568,
%T A381347 323581504,4554426368,51666451456,458243735552,2004840714496,
%U A381347 -37024075153408,-1386061762251776,-29290212127670272,-483475390212586496,-6224109737622372352,-45231727252157947904
%N A381347 Expansion of e.g.f. 1/( 1 - sin(sqrt(2)*x) / sqrt(2) ).
%F A381347 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-2)^k * binomial(n,2*k+1) * a(n-2*k-1).
%F A381347 a(n) = Sum_{k=0..n} k! * (-2)^((n-k)/2) * A136630(n,k)
%o A381347 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381347 a(n) = sum(k=0, n, k!*(-2)^((n-k)/2)*a136630(n, k));
%Y A381347 Cf. A191277, A381284, A381285, A381286, A381346.
%Y A381347 Cf. A136630, A263249.
%K A381347 sign
%O A381347 0,3
%A A381347 _Seiichi Manyama_, Feb 20 2025