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 A385632 #31 Aug 16 2025 10:03:17
%S A385632 1,8,81,872,9669,109128,1246419,14359304,166512285,1940885504,
%T A385632 22717923586,266833238328,3143237113479,37119019790016,
%U A385632 439290932937672,5208668386199112,61861932606093901,735804601177846968,8763478151940329859,104498114621004830160,1247410783999193335434
%N A385632 a(n) = Sum_{k=0..n} 2^(n-k) * binomial(5*n+1,k).
%F A385632 a(n) = [x^n] 1/((1-3*x) * (1-x)^(4*n+1)).
%F A385632 a(n) = Sum_{k=0..n} 3^(n-k) * binomial(4*n+k,k).
%F A385632 a(n) = 3^(5*n+1)*2^(-4*n-1) - binomial(5*n+1, n)*(hypergeom([1, -1-4*n], [1+n], -1/2) - 1). - _Stefano Spezia_, Aug 05 2025
%F A385632 a(n) = Sum_{k=0..n} 3^k * (-2)^(n-k) * binomial(5*n+1,k) * binomial(5*n-k,n-k). - _Seiichi Manyama_, Aug 07 2025
%F A385632 G.f.: g^2/((3-2*g) * (5-4*g)) where g = 1+x*g^5 is the g.f. of A002294. - _Seiichi Manyama_, Aug 14 2025
%F A385632 From _Seiichi Manyama_, Aug 16 2025: (Start)
%F A385632 G.f.: 1/(1 - x*g^3*(15-7*g)) where g = 1+x*g^5 is the g.f. of A002294.
%F A385632 G.f.: B(x)^2/(1 + 2*(B(x)-1)/5), where B(x) is the g.f. of A001449. (End)
%o A385632 (PARI) a(n) = sum(k=0, n, 2^(n-k)*binomial(5*n+1, k));
%Y A385632 Cf. A006256, A141223, A385605.
%Y A385632 Cf. A001449, A079589, A079678, A371753, A386812.
%Y A385632 Cf. A386699.
%K A385632 nonn
%O A385632 0,2
%A A385632 _Seiichi Manyama_, Aug 03 2025