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 A381343 #15 Feb 21 2025 05:50:47
%S A381343 1,1,1,-1,-7,-15,25,287,721,-2847,-30255,-61697,682761,5861713,
%T A381343 3105193,-258188513,-1681060063,4623681473,135471132705,564325398271,
%U A381343 -6357495670375,-89817656595791,-84337394884167,7820620314702879,67277670159083761,-322108989883888479
%N A381343 Expansion of e.g.f. exp( sin(sqrt(2)*x) / sqrt(2) ).
%F A381343 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-2)^k * binomial(n-1,2*k) * a(n-2*k-1).
%F A381343 a(n) = Sum_{k=0..n} (-2)^((n-k)/2) * A136630(n,k).
%o A381343 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381343 a(n) = sum(k=0, n, (-2)^((n-k)/2)*a136630(n, k));
%Y A381343 Cf. A002017, A009210, A009229, A351891, A351892, A381277, A381278, A381280, A381344.
%Y A381343 Cf. A136630.
%K A381343 sign
%O A381343 0,5
%A A381343 _Seiichi Manyama_, Feb 20 2025