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 A370378 #17 Mar 29 2025 07:09:18
%S A370378 1,2,28,824,44080,3837536,496714432,89388391808,21308786907904,
%T A370378 6492490191541760,2459980247094946816,1134165248844198336512,
%U A370378 625104522913814858149888,405845822590303335956701184,306541019968859037778756157440
%N A370378 Number of compositions of n where there are (2*k)! sorts of part k.
%F A370378 G.f.: 1 / (1 - Sum_{k>=1} (2*k)! * x^k).
%F A370378 a(0) = 1; a(n) = Sum_{k=1..n} (2*k)! * a(n-k).
%F A370378 a(n) ~ (2*n)! * (1 + 1/n^2 + 1/(2*n^3) + 4/n^4 + 91/(8*n^5) + 51/n^6 + 7951/(32*n^7) + 11147/(8*n^8) + 1122171/(128*n^9) + 983245/(16*n^10) + ...). - _Vaclav Kotesovec_, Feb 17 2024
%t A370378 nmax = 15; CoefficientList[Series[1/(1 - Sum[(2*k)! * x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 17 2024 *)
%o A370378 (PARI) my(N=20, x='x+O('x^N)); Vec(1/(1-sum(k=1, N, (2*k)!*x^k)))
%Y A370378 Cf. A051296, A010050, A370379.
%K A370378 nonn,easy
%O A370378 0,2
%A A370378 _Seiichi Manyama_, Feb 17 2024