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 A381908 #10 Mar 10 2025 07:02:32
%S A381908 1,2,9,64,556,5351,54818,585941,6459430,72902748,838174008,9781930978,
%T A381908 115579403512,1379879992445,16620303073607,201717610488447,
%U A381908 2464502123154530,30286289207099652,374115157763376043,4642636869759251879,57852132860181652189,723592983110972398779
%N A381908 Expansion of (1/x) * Series_Reversion( x / ((1+x) * B(x)) ), where B(x) is the g.f. of A002293.
%F A381908 G.f. A(x) satisfies A(x) = (1 + x*A(x)) * B(x*A(x)).
%F A381908 a(n) = Sum_{k=0..n} binomial(n+4*k+1,k) * binomial(n+1,n-k)/(n+4*k+1).
%F A381908 a(n) = hypergeom([(1+n)/4, (2+n)/4, (3+n)/4, (4+n)/4, -n], [2, (2+n)/3, (3+n)/3, (4+n)/3], -2^8/3^3). - _Stefano Spezia_, Mar 10 2025
%o A381908 (PARI) a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(n+1, n-k)/(n+4*k+1));
%Y A381908 Cf. A381909, A381910.
%Y A381908 Cf. A002293.
%K A381908 nonn
%O A381908 0,2
%A A381908 _Seiichi Manyama_, Mar 10 2025