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 A371739 #37 Aug 17 2025 09:53:15
%S A371739 1,6,56,576,6196,68406,768212,8731848,100146724,1156626990,
%T A371739 13432735556,156713948672,1835237017324,21560768699762,
%U A371739 253994850228896,2999267652451776,35490014668470052,420718526924212654,4995548847105422048,59402743684137281920
%N A371739 a(n) = Sum_{k=0..n} binomial(5*n,k).
%F A371739 a(n) = [x^n] 1/((1-2*x) * (1-x)^(4*n)).
%F A371739 a(n) ~ 5^(5*n + 1/2) / (3*sqrt(Pi*n) * 2^(8*n - 1/2)). - _Vaclav Kotesovec_, Apr 05 2024
%F A371739 a(n) = Sum_{k=0..floor(n/2)} binomial(5*n+1,n-2*k). - _Seiichi Manyama_, Apr 09 2024
%F A371739 a(n) = binomial(1+5*n, n)*hypergeom([1, (1-n)/2, -n/2], [1+2*n, 3/2+2*n], 1). - _Stefano Spezia_, Apr 09 2024
%F A371739 a(n) = Sum_{k=0..n} 2^(n-k) * binomial(4*n+k-1,k). - _Seiichi Manyama_, Jul 30 2025
%F A371739 a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(5*n,k) * binomial(5*n-k-1,n-k). - _Seiichi Manyama_, Aug 08 2025
%F A371739 G.f.: g/((2-g) * (5-4*g)) where g = 1+x*g^5 is the g.f. of A002294. - _Seiichi Manyama_, Aug 12 2025
%F A371739 G.f.: 1/(1 - x*g^4*(10-4*g)) where g = 1+x*g^5 is the g.f. of A002294. - _Seiichi Manyama_, Aug 17 2025
%t A371739 Table[32^n - Binomial[5*n, 1+n] * Hypergeometric2F1[1, 1 - 4*n, 2+n, -1], {n, 0, 20}] (* _Vaclav Kotesovec_, Apr 05 2024 *)
%o A371739 (PARI) a(n) = sum(k=0, n, binomial(5*n, k));
%Y A371739 Cf. A032443, A066380, A066381.
%Y A371739 Cf. A002294, A163455, A386699.
%K A371739 nonn,easy
%O A371739 0,2
%A A371739 _Seiichi Manyama_, Apr 05 2024