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 A375954 #11 May 20 2025 02:31:13
%S A375954 1,5,40,425,5605,88100,1606015,33291725,773093830,19875432575,
%T A375954 560334083965,17187010139150,569768238573805,20299523526975425,
%U A375954 773470729977309040,31385122689116278325,1351135296804805544905,61507193821772778512900
%N A375954 Expansion of e.g.f. 1 / (3 - 2 * exp(x))^(5/2).
%F A375954 a(n) = (1/3) * Sum_{k=0..n} A001147(k+2) * Stirling2(n,k).
%F A375954 a(n) ~ 2^(5/2) * n^(n+2) / (3^(7/2) * log(3/2)^(n + 5/2) * exp(n)). - _Vaclav Kotesovec_, May 20 2025
%t A375954 nmax=17; CoefficientList[Series[1 / (3 - 2 * Exp[x])^(5/2),{x,0,nmax}],x]*Range[0,nmax]! (* _Stefano Spezia_, Sep 03 2024 *)
%o A375954 (PARI) a001147(n) = prod(k=0, n-1, 2*k+1);
%o A375954 a(n) = sum(k=0, n, a001147(k+2)*stirling(n, k, 2))/3;
%Y A375954 Cf. A004123, A367470, A367471, A375948.
%Y A375954 Cf. A001147.
%K A375954 nonn
%O A375954 0,2
%A A375954 _Seiichi Manyama_, Sep 03 2024