A365184 - OEIS

%I #15 Nov 01 2023 10:00:58

%S 1,1,6,45,395,3775,38146,400826,4335455,47951065,539823620,6165377836,

%T 71261299056,831990025420,9797505040130,116235417614900,

%U 1387958781395535,16668362761081560,201190667288072005,2439418470063468505,29698136499328762445

%N G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x).

%H Seiichi Manyama, <a href="/A365184/b365184.txt">Table of n, a(n) for n = 0..898</a>

%F a(n) = Sum_{k=0..n} binomial(5*k+1,k) * binomial(k,n-k)/(5*k+1) = Sum_{k=0..n} binomial(k,n-k) * A002294(k).

%o (PARI) a(n) = sum(k=0, n, binomial(k, n-k)*binomial(5*k, k)/(4*k+1));

%Y Cf. A002295, A365185, A365186, A365187, A365188, A365189.

%Y Cf. A364475, A365178.

%Y Cf. A002294, A349332.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 25 2023