OFFSET
0,2
FORMULA
E.g.f.: exp(-1 + Product_{k>=1} (1 + x^k)/(1 - x^k)).
a(0) = 1; a(n) = Sum_{k=1..n} A015128(k)*k!*binomial(n-1,k-1)*a(n-k).
MAPLE
seq(coeff(series(factorial(n)*(exp(-1+mul((1+x^k)/(1-x^k), k=1..n))), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 23 2018
MATHEMATICA
nmax = 19; CoefficientList[Series[Exp[1/EllipticTheta[4, 0, x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Sum[PartitionsP[k - j] PartitionsQ[j], {j, 0, k}] k! Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 19}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 23 2018
STATUS
approved