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 A381277 #8 Feb 19 2025 03:37:22
%S A381277 1,1,1,10,37,172,1477,8416,74377,683344,5836969,67102048,699721453,
%T A381277 8268521536,107106298093,1347611617792,19462095444241,279380302430464,
%U A381277 4247519795325649,68946703997616640,1122787065355425973,19697500164381137920,351304020205694058133
%N A381277 Expansion of e.g.f. exp(sinh(3*x) / 3).
%F A381277 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 A381277 a(n) = Sum_{k=0..n} 3^(n-k) * A136630(n,k).
%o A381277 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381277 a(n) = sum(k=0, n, 3^(n-k)*a136630(n, k));
%Y A381277 Cf. A003724, A009229.
%Y A381277 Cf. A136630.
%K A381277 nonn
%O A381277 0,4
%A A381277 _Seiichi Manyama_, Feb 18 2025