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 A381775 #12 Mar 08 2025 02:30:52
%S A381775 1,2,27,523,11871,294668,7747698,212054604,5978347887,172421233231,
%T A381775 5063192676597,150872475295522,4550458484780442,138652322209300991,
%U A381775 4261638256558924407,131973650298641750844,4113788296015093994719,128973000885015536107140
%N A381775 Expansion of ( (1/x) * Series_Reversion( x/((1+x) * C(x))^6 ) )^(1/6), where C(x) is the g.f. of A000108.
%F A381775 G.f. A(x) satisfies A(x) = (1 + x*A(x)^6) * C(x*A(x)^6).
%F A381775 a(n) = Sum_{k=0..n} binomial(6*n+2*k+1,k) * binomial(6*n+1,n-k)/(6*n+2*k+1).
%F A381775 a(n) = binomial(1 + 6*n, n)*hypergeom([-n, 1/2+3*n, 1+3*n], [2+5*n, 2+6*n], -4)/(1 + 6*n). - _Stefano Spezia_, Mar 07 2025
%o A381775 (PARI) my(N=20, x='x+O('x^N)); Vec((serreverse(x/((1+x)*(1-sqrt(1-4*x))/(2*x))^6)/x)^(1/6))
%Y A381775 Cf. A054727, A060941, A381772, A381773, A381774.
%Y A381775 Cf. A000108.
%K A381775 nonn
%O A381775 0,2
%A A381775 _Seiichi Manyama_, Mar 07 2025