A365732 - OEIS

%I #16 Sep 18 2023 08:59:27

%S 1,1,1,1,1,1,2,5,11,21,36,57,88,142,250,473,917,1751,3240,5829,10350,

%T 18472,33574,62293,117138,220932,414777,773282,1434776,2661302,

%U 4955167,9279325,17466103,32971057,62274094,117521503,221572762,417699772,788205724,1489975777

%N G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^5*A(x)^2).

%H Seiichi Manyama, <a href="/A365732/b365732.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = Sum_{k=0..floor(n/6)} binomial(n-5*k,k) * binomial(n-3*k+1,n-5*k) / (n-3*k+1) = Sum_{k=0..floor(n/6)} binomial(n-3*k,3*k) * binomial(3*k,k) / (2*k+1).

%o (PARI) a(n) = sum(k=0, n\6, binomial(n-5*k, k)*binomial(n-3*k+1, n-5*k)/(n-3*k+1));

%Y Cf. A000108, A071879, A364552, A365252.

%Y Cf. A001764, A365734.

%K nonn

%O 0,7

%A _Seiichi Manyama_, Sep 17 2023