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 A346672 #14 Jul 30 2021 10:19:51
%S A346672 1,2,10,102,1342,19620,305004,4943352,82595376,1412486081,24602515801,
%T A346672 434935956337,7783978950825,140752989839105,2567623696254905,
%U A346672 47195200645619009,873239636055018809,16251426606785706209,304007720310330530081,5713101394865420846381
%N A346672 a(n) = Sum_{k=0..n} binomial(8*k,k) / (7*k + 1).
%C A346672 Partial sums of A007556.
%C A346672 In general, for m > 1, Sum_{k=0..n} binomial(m*k,k) / ((m-1)*k + 1) ~ m^(m*(n+1) + 1/2) / (sqrt(2*Pi) * (m^m - (m-1)^(m-1)) * n^(3/2) * (m-1)^((m-1)*n + 3/2)). - _Vaclav Kotesovec_, Jul 30 2021
%H A346672 Seiichi Manyama, <a href="/A346672/b346672.txt">Table of n, a(n) for n = 0..768</a>
%F A346672 G.f. A(x) satisfies: A(x) = 1 / (1 - x) + x * (1 - x)^7 * A(x)^8.
%F A346672 a(n) ~ 2^(24*n + 25) / (15953673 * sqrt(Pi) * n^(3/2) * 7^(7*n + 3/2)). - _Vaclav Kotesovec_, Jul 30 2021
%t A346672 Table[Sum[Binomial[8 k, k]/(7 k + 1), {k, 0, n}], {n, 0, 19}]
%t A346672 nmax = 19; A[_] = 0; Do[A[x_] = 1/(1 - x) + x (1 - x)^7 A[x]^8 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%o A346672 (PARI) a(n) = sum(k=0, n, binomial(8*k, k)/(7*k+1)); \\ _Michel Marcus_, Jul 28 2021
%Y A346672 Cf. A007556, A014137, A104859, A345367, A345368, A346065, A346650, A346671.
%K A346672 nonn
%O A346672 0,2
%A A346672 _Ilya Gutkovskiy_, Jul 28 2021