login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A364041
Expansion of 1/Product_{k>0} (1 - x^(2*k-1))^((2*k-1)^(2*k-1)).
1
1, 1, 1, 28, 28, 3153, 3531, 827074, 911449, 388335592, 415455628, 285728307489, 298762259972, 303174312029604, 312427539531172, 438206538943092800, 447594828079035405, 827688010429432132457, 840767646450714838158, 1979260573433349667269165
OFFSET
0,4
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).
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 *)
PROG
(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))))
CROSSREFS
Sequence in context: A022362 A219914 A165849 * A093681 A044874 A022398
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 09 2023
STATUS
approved