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 A381179 #8 Feb 16 2025 10:06:03 %S A381179 1,1,0,1,8,21,64,1093,8448,47785,654848,9402537,94222336,1264390141, %T A381179 23392960512,363389219053,5722054885376,117602664867921, %U A381179 2434091053613056,47867013812467921,1080303165427679232,26716998341391367141,645003218568158904320,16403742152044108508181 %N A381179 E.g.f. A(x) satisfies A(x) = 1 + sinh(x*A(x)) / A(x). %F A381179 a(n) = Sum_{k=0..n} k! * binomial(n-k+1,k)/(n-k+1) * A136630(n,k). %o A381179 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j)); %o A381179 a(n) = sum(k=0, n, k!*binomial(n-k+1, k)/(n-k+1)*a136630(n, k)); %Y A381179 Cf. A162653, A201628, A381177. %Y A381179 Cf. A136630, A196776. %K A381179 nonn %O A381179 0,5 %A A381179 _Seiichi Manyama_, Feb 16 2025