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 A107404 #24 Mar 07 2025 06:33:18
%S A107404 1,2,6,26,144,962,7536,67706,685824,7730882,95970816,1300815386,
%T A107404 19113775104,302616787202,5135568746496,92996021795066,
%U A107404 1789758460329984,36479831022049922,785020114093080576,17785273588395966746,423150055005134782464,10548427254444904799042
%N A107404 Expansion of e.g.f. 1/(1 - sinh(x))^2.
%F A107404 a(n) = D^n(1/(1-x)^2) evaluated at x = 0, where D is the operator sqrt(1+x^2)*d/dx. Cf. A006154. - _Peter Bala_, Dec 06 2011
%F A107404 a(n) ~ n!*n/(2*(log(1+sqrt(2)))^(n+2)). - _Vaclav Kotesovec_, Jun 27 2013
%F A107404 a(n) = Sum_{k=0..n} (k+1)! * A136630(n,k). - _Seiichi Manyama_, Feb 17 2025
%p A107404 E(x):=1/(1-sinh(x))^2: f[0]:=E(x): for n from 1 to 30 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..30);
%t A107404 CoefficientList[Series[1/(1-Sinh[x])^2, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 27 2013 *)
%o A107404 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A107404 a(n) = sum(k=0, n, (k+1)!*a136630(n, k)); \\ _Seiichi Manyama_, Feb 17 2025
%Y A107404 Cf. A000557. A006154, A136630.
%K A107404 nonn
%O A107404 0,2
%A A107404 _Miklos Kristof_, Jun 09 2005