%I #13 Jan 25 2023 09:07:51
%S 1,1,6,21,71,251,882,3088,10829,37975,133146,466852,1636944,5739647,
%T 20125051,70564951,247423522,867546829,3041899638,10665883415,
%U 37398034921,131129599227,459782762029,1612146986543,5652708454881,19820223058176,69496108849357
%N a(n) = Sum_{k=0..n} binomial(5*k,n-k).
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,10,10,5,1).
%F a(n) = a(n-1) + 5*a(n-2) + 10*a(n-3) + 10*a(n-4) + 5*a(n-5) + a(n-6).
%F G.f.: 1/(1 - x*(1+x)^5).
%o (PARI) a(n) = sum(k=0, n, binomial(5*k, n-k));
%o (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-x*(1+x)^5))
%Y Cf. A002478, A099234, A099235.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Jan 25 2023