A345871 Expansion of e.g.f. Product_{k>=1} ((1 + x^k)/(1 - x^k))^(1/(2*k!)).

1, 1, 2, 7, 23, 116, 707, 4775, 34092, 326723, 3255927, 35131570, 404387205, 5178352921, 72399248378, 1124473250815, 17051538263075, 287692287405292, 5225129815132463, 97469631563584567, 1891891950093538380, 40846072052629411027, 895935864764993940483

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..450

Formula

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

Prog

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

Crossrefs

Cf. A005408, A206303, A209902, A298906, A345870.

Sequence in context: A006986 A000903 A049021 * A375130 A332802 A002494

Adjacent sequences: A345868 A345869 A345870 * A345872 A345873 A345874

Keyword

nonn

Author

Seiichi Manyama, Jun 27 2021

Status

approved