A345870 Expansion of e.g.f. Product_{k>=1} ((1 + x^k)/(1 - x^k))^(1/k!).

1, 2, 6, 26, 126, 742, 5166, 40462, 351742, 3458470, 37425406, 440788702, 5633316574, 77379974518, 1140707915262, 18053421105742, 302414295475134, 5364631473148614, 100769601500958078, 1988246969908681278, 41179474537324087454, 896909297854081874454

Offset: 0

Author

Seiichi Manyama, Jun 27 2021

Keywords

• nonn

Comments

Exponential convolution of the sequences A209902 and A298906.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A005408, A209902, A295792, A298906, A306041, A345871.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, ((1+x^k)/(1-x^k))^(1/k!))))

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(2*sum(k=0, N\2, (exp(x^(2*k+1))-1)/(2*k+1)))))

Formula

E.g.f.: exp( 2*Sum_{k>=0} (exp(x^(2*k+1)) - 1)/(2*k+1) ).