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 A381910 #12 Mar 10 2025 07:03:49
%S A381910 1,4,26,222,2243,25243,305217,3878731,51097713,691596081,9558970897,
%T A381910 134347855874,1914131985782,27582542400252,401284140631911,
%U A381910 5886072268606617,86951528919335670,1292467847124221832,19316795168721092789,290107272994659617741,4375905051887803660504
%N A381910 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * B(x)) ), where B(x) is the g.f. of A002293.
%F A381910 G.f. A(x) satisfies A(x) = (1 + x*A(x))^3 * B(x*A(x)).
%F A381910 a(n) = Sum_{k=0..n} binomial(n+4*k+1,k) * binomial(3*n+3,n-k)/(n+4*k+1).
%F A381910 a(n) = binomial(3*(1 + n), n)*hypergeom([(1+n)/4, (2+n)/4, (3+n)/4, (4+n)/4, -n], [(2+n)/3, (3+n)/3, (4+n)/3, 4+2*n], -2^8/3^3)/(1 + n). - _Stefano Spezia_, Mar 10 2025
%o A381910 (PARI) a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(3*n+3, n-k)/(n+4*k+1));
%Y A381910 Cf. A381908, A381909.
%Y A381910 Cf. A002293.
%K A381910 nonn
%O A381910 0,2
%A A381910 _Seiichi Manyama_, Mar 10 2025