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 A370058 #23 Feb 06 2025 12:34:41
%S A370058 1,4,44,840,23256,850080,38750400,2120489280,135566323200,
%T A370058 9922550077440,818544054182400,75160674504115200,7604312776752384000,
%U A370058 840608992488545280000,100812386907863414784000,13037431708092153922560000,1808675231786149165350912000
%N A370058 a(n) = 4*(4*n+3)!/(3*n+4)!.
%F A370058 E.g.f.: exp( Sum_{k>=1} binomial(4*k,k) * x^k/k ).
%F A370058 a(n) = A000142(n) * A002293(n+1).
%F A370058 D-finite with recurrence 3*(3*n+2)*(3*n+4)*(n+1)*a(n) -8*n*(4*n+1)*(2*n+1)*(4*n+3)*a(n-1)=0. - _R. J. Mathar_, Feb 22 2024
%F A370058 From _Seiichi Manyama_, Aug 31 2024: (Start)
%F A370058 E.g.f. satisfies A(x) = 1/(1 - x*A(x)^(3/4))^4.
%F A370058 a(n) = 4 * Sum_{k=0..n} (3*n+4)^(k-1) * |Stirling1(n,k)|. (End)
%F A370058 E.g.f.: (1/x) * Series_Reversion( x/(1 + x)^4 ). - _Seiichi Manyama_, Feb 06 2025
%o A370058 (PARI) a(n) = 4*(4*n+3)!/(3*n+4)!;
%Y A370058 Cf. A365340, A370056, A370057.
%Y A370058 Cf. A065866, A370055.
%Y A370058 Cf. A000142, A002293.
%K A370058 nonn
%O A370058 0,2
%A A370058 _Seiichi Manyama_, Feb 08 2024