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 A361303 #7 Mar 09 2023 09:00:50
%S A361303 1,2,15,92,615,4200,29190,205416,1458909,10436030,75079719,542669244,
%T A361303 3937604853,28664996080,209261546580,1531373181120,11230365782130,
%U A361303 82512324300222,607246350958449,4475646134515360,33031356134381220,244073892799489500,1805479496422561740
%N A361303 Expansion of g.f. A(x) = Sum_{n>=0} d^n/dx^n x^(2*n) * (1 + x)^(3*n) / n!.
%F A361303 G.f. A(x) = Sum_{n>=0} a(n)*x^n may be defined by the following.
%F A361303 (1) A(x) = Sum_{n>=0} d^n/dx^n x^(2*n) * (1 + x)^(3*n) / n!.
%F A361303 (2) A(x) = d/dx Series_Reversion(x - x^2*(1 + x)^3).
%F A361303 (3) B(x - x^2*A(x)^3) = x where B(x) = x * exp( Sum_{n>=1} d^(n-1)/dx^(n-1) x^(2*n-1) * (1+x)^(3*n) / n! ) is the g.f. of A361305.
%F A361303 (4) a(n) = (n+1) * A361305(n+1) for n >= 0.
%e A361303 G.f.: A(x) = 1 + 2*x + 15*x^2 + 92*x^3 + 615*x^4 + 4200*x^5 + 29190*x^6 + 205416*x^7 + 1458909*x^8 + 10436030*x^9 + ...
%o A361303 (PARI) {Dx(n, F) = my(D=F); for(i=1, n, D=deriv(D)); D}
%o A361303 {a(n) = my(A=1); A = sum(m=0, n, Dx(m, x^(2*m)*(1+x +O(x^(n+1)))^(3*m)/m!)); polcoeff(A, n)}
%o A361303 for(n=0, 25, print1(a(n), ", "))
%o A361303 (PARI) /* Using series reversion (faster) */
%o A361303 {a(n) = my(A=1); A = deriv( serreverse(x - x^2*(1+x +O(x^(n+3)))^3 )); polcoeff(A, n)}
%o A361303 for(n=0, 25, print1(a(n), ", "))
%Y A361303 Cf. A361305, A215128, A361046.
%K A361303 nonn
%O A361303 0,2
%A A361303 _Paul D. Hanna_, Mar 08 2023