A395657 - OEIS

%I #8 May 03 2026 10:17:22

%S 1,15,215,2995,40914,551005,7340200,96943515,1271426915,16578465406,

%T 215115348570,2779579995425,35785838757200,459266020152120,

%U 5877599725713264,75033029204530155,955728484127802825,12149038561177186525,154154652693004201225,1952762911533701935206

%N Expansion of 1/(16*x) * (1/(5-4*g)^4 - 1), where g = 1+x*g^5 is the g.f. of A002294.

%F a(n) = A395660(n)/(n+1) = (1/(n+1)) * Sum_{k=0..n} 4^k * binomial(k+4,4) * binomial(5*n+5,n-k).

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

%Y Cf. A001700, A395655, A395656.

%Y Cf. A002294, A359660.

%K nonn

%O 0,2

%A _Seiichi Manyama_, May 02 2026