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 A375948 #15 May 20 2025 02:30:11
%S A375948 1,3,18,153,1683,22698,362403,6683463,139787568,3269240883,
%T A375948 84535585263,2394699999948,73749495626253,2453332830142743,
%U A375948 87667856626175298,3349116499958627733,136209377351085310863,5875794769594996985778,267968680043585007829383
%N A375948 Expansion of e.g.f. 1 / (3 - 2 * exp(x))^(3/2).
%F A375948 a(n) = Sum_{k=0..n} A001147(k+1) * Stirling2(n,k).
%F A375948 a(n) ~ 2^(3/2) * n^(n+1) / (3^(3/2) * log(3/2)^(n + 3/2) * exp(n)). - _Vaclav Kotesovec_, May 20 2025
%t A375948 nmax=18; CoefficientList[Series[1 / (3 - 2 * Exp[x])^(3/2),{x,0,nmax}],x]*Range[0,nmax]! (* _Stefano Spezia_, Sep 03 2024 *)
%o A375948 (PARI) a001147(n) = prod(k=0, n-1, 2*k+1);
%o A375948 a(n) = sum(k=0, n, a001147(k+1)*stirling(n, k, 2));
%Y A375948 Cf. A005649, A375949.
%Y A375948 Cf. A004123, A367470, A367471, A375954.
%Y A375948 Cf. A001147.
%K A375948 nonn
%O A375948 0,2
%A A375948 _Seiichi Manyama_, Sep 03 2024