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 A381284 #10 Apr 19 2025 06:00:02
%S A381284 1,1,2,15,96,741,7632,87795,1149696,17155881,282880512,5128464375,
%T A381284 101592631296,2178698451021,50314379323392,1245198047833755,
%U A381284 32868161979088896,921803465256094161,27373850876851126272,858044392807801699935,28311289100161039466496
%N A381284 Expansion of e.g.f. 1/(1 - sinh(3*x) / 3).
%F A381284 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 9^k * binomial(n,2*k+1) * a(n-2*k-1).
%F A381284 a(n) = Sum_{k=0..n} k! * 3^(n-k) * A136630(n,k).
%F A381284 a(n) ~ sqrt(Pi/5) * 3^(n+1) * n^(n + 1/2) / (arcsinh(3)^(n+1) * exp(n)). - _Vaclav Kotesovec_, Apr 19 2025
%o A381284 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381284 a(n) = sum(k=0, n, k!*3^(n-k)*a136630(n, k));
%Y A381284 Cf. A006154, A191277.
%Y A381284 Cf. A136630.
%K A381284 nonn
%O A381284 0,3
%A A381284 _Seiichi Manyama_, Feb 18 2025