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 A381278 #10 Feb 19 2025 03:37:37
%S A381278 1,1,1,-8,-35,-8,1117,6328,-19943,-513728,-2096711,30574720,447401845,
%T A381278 23791744,-59033858219,-527680180736,4971322421425,144677554315264,
%U A381278 430091284739185,-27641200139694080,-398305237630617971,2876369985206861824,145441158283475935309
%N A381278 Expansion of e.g.f. exp(sin(3*x) / 3).
%F A381278 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-9)^k * binomial(n-1,2*k) * a(n-2*k-1).
%F A381278 a(n) = Sum_{k=0..n} (3*i)^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381278 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381278 a(n) = sum(k=0, n, (3*I)^(n-k)*a136630(n, k));
%Y A381278 Cf. A002017, A009210.
%Y A381278 Cf. A136630, A352640, A381286.
%K A381278 sign
%O A381278 0,4
%A A381278 _Seiichi Manyama_, Feb 18 2025