A395656 - OEIS

%I #8 May 03 2026 10:17:52

%S 1,10,100,995,9852,97144,954540,9351945,91397260,891337624,8676673168,

%T 84327075545,818401761220,7932693938760,76804617216840,

%U 742874557254885,7178721120223020,69313564579177240,668744574950480560,6447636717495742540,62124533086188443760

%N Expansion of 1/(9*x) * (1/(4-3*g)^3 - 1), where g = 1+x*g^4 is the g.f. of A002293.

%F a(n) = A395659(n)/(n+1) = (1/(n+1)) * Sum_{k=0..n} 3^k * binomial(k+3,3) * binomial(4*n+4,n-k).

%o (PARI) a(n) = sum(k=0, n, 3^k*binomial(k+3, 3)*binomial(4*n+4, n-k))/(n+1);

%Y Cf. A001700, A395655, A395657.

%Y Cf. A002293, A395659.

%K nonn

%O 0,2

%A _Seiichi Manyama_, May 02 2026