A364041 Expansion of 1/Product_{k>0} (1 - x^(2*k-1))^((2*k-1)^(2*k-1)).

1, 1, 1, 28, 28, 3153, 3531, 827074, 911449, 388335592, 415455628, 285728307489, 298762259972, 303174312029604, 312427539531172, 438206538943092800, 447594828079035405, 827688010429432132457, 840767646450714838158, 1979260573433349667269165

Offset: 0

Author

Seiichi Manyama, Jul 09 2023

Keywords

• nonn

Crossrefs

Cf. A023880, A363991.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[DivisorSum[k, #^(# + 1) &, OddQ[#] &]*a[n - k], {k, 1, n}]/n; Array[a, 20, 0] (* Amiram Eldar, Jul 09 2023 *)

PARI

my(N=20, x='x+O('x^N)); Vec(1/prod(k=1, N, (1-x^(2*k-1))^((2*k-1)^(2*k-1))))

Formula

G.f.: exp( Sum_{k>0} A363991(k) * x^k/k ).

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} A363991(k) * a(n-k).