A384357 - OEIS

%I #11 May 27 2025 10:33:14

%S 1,1,153,128793,319155321,1744213657689,17803590830142393,

%T 304609764628470426969,8095576593110601916260369,

%U 315845539893724747798646514673,17317064152543324914717101316522961,1288754843591816442932799782872809777393,126555732798742295186573610437899751882638209

%N Expansion of Product_{k>=1} 1/(1 - k*(k+1)*(k+2)/6 * x)^((1/54) * (2/3)^k).

%F G.f.: exp((1/8) * Sum_{k>=1} A384362(3,k) * x^k/k).

%o (PARI) a384362(n, k) = sum(i=0, k*n, 2^i*sum(j=0, i, (-1)^j*binomial(i, j)*binomial(i-j, n)^k));

%o my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, a384362(3, k)*x^k/k)/8))

%Y Cf. A384362.

%K nonn

%O 0,3

%A _Seiichi Manyama_, May 27 2025