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 A381280 #12 Apr 19 2025 07:16:15
%S A381280 1,1,2,18,120,920,10320,126448,1714048,27073152,472354560,8989147904,
%T A381280 187690331136,4245706716160,103239264593920,2691918892861440,
%U A381280 74885151106498560,2212607133043884032,69227613551324233728,2286465386258267176960,79487593489348266557440
%N A381280 Expansion of e.g.f. 1/(1 - x * cosh(2*x)).
%C A381280 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381280 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 4^k * (2*k+1) * binomial(n,2*k+1) * a(n-2*k-1).
%F A381280 a(n) = Sum_{k=0..n} k! * 2^(n-k) * A185951(n,k).
%F A381280 a(n) ~ sqrt(Pi) * 2^(n + 5/2) * n^(n + 1/2) / ((1 + sinh(r))^2 * exp(n) * r^(n+2)), where r = A201939. - _Vaclav Kotesovec_, Apr 19 2025
%o A381280 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381280 a(n) = sum(k=0, n, k!*2^(n-k)*a185951(n, k));
%Y A381280 Cf. A205571, A381281.
%Y A381280 Cf. A185951, A201939.
%K A381280 nonn
%O A381280 0,3
%A A381280 _Seiichi Manyama_, Feb 18 2025