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 A375952 #10 Sep 03 2024 12:13:57 %S A375952 1,5,45,565,9085,177925,4106445,109105365,3279219485,109983317925, %T A375952 4071784884845,164919693538165,7253726995805885,344284133391481925, %U A375952 17538600019076063245,954467594134586386965,55263075631036363208285,3391909484128563111709925 %N A375952 Expansion of e.g.f. 1 / (4 - 3 * exp(x))^(5/3). %F A375952 a(n) = (1/2) * Sum_{k=0..n} A008544(k+1) * Stirling2(n,k). %t A375952 nmax=17; CoefficientList[Series[1 / (4 - 3 * Exp[x])^(5/3),{x,0,nmax}],x]*Range[0,nmax]! (* _Stefano Spezia_, Sep 03 2024 *) %o A375952 (PARI) a008544(n) = prod(k=0, n-1, 3*k+2); %o A375952 a(n) = sum(k=0, n, a008544(k+1)*stirling(n, k, 2))/2; %Y A375952 Cf. A032033, A346982, A365558, A375949. %Y A375952 Cf. A008544. %K A375952 nonn %O A375952 0,2 %A A375952 _Seiichi Manyama_, Sep 03 2024