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 A370379 #16 Mar 29 2025 07:09:13
%S A370379 1,1,13,385,21061,1864921,243833533,44133789745,10556951897461,
%T A370379 3223557261840841,1223184443268467053,564530822421956927905,
%U A370379 311384269987431969105061,202282520358685311116600761,152856358784713560205903602973
%N A370379 Number of compositions of n where there are (2*k)!/2 sorts of part k.
%F A370379 G.f.: 1 / (1 - Sum_{k>=1} (2*k)!/2 * x^k).
%F A370379 a(0) = 1; a(n) = Sum_{k=1..n} (2*k)!/2 * a(n-k).
%o A370379 (PARI) my(N=20, x='x+O('x^N)); Vec(1/(1-sum(k=1, N, (2*k)!/2*x^k)))
%Y A370379 Cf. A002674, A051295, A370378.
%K A370379 nonn,easy
%O A370379 0,3
%A A370379 _Seiichi Manyama_, Feb 17 2024