A330540 Expansion of e.g.f. Product_{k>=1} (1 + arcsinh(x^k)).

1, 1, 2, 11, 48, 349, 2640, 23673, 231504, 2693241, 33313680, 446104845, 6572693160, 103319528805, 1750718151000, 31865325610545, 607019625223200, 12253084499034225, 263721891513921120, 5900460781451357205, 139338570648068278200

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 + ArcSinh[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 20; CoefficientList[Series[Exp[Sum[Sum[(-1)^(d + 1) ArcSinh[x^(k/d)]^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A001818, A270294, A330539.

Sequence in context: A003442 A054894 A270662 * A139475 A034568 A265610

Adjacent sequences: A330537 A330538 A330539 * A330541 A330542 A330543

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 17 2019

Status

approved