A302606 a(n) = n! * [x^n] exp(n*x)*arcsinh(x).

0, 1, 4, 26, 240, 2884, 42660, 748544, 15185856, 349574544, 9000902500, 256293989984, 7996078704240, 271246034903232, 9939835626507332, 391303051339622400, 16469438021801262848, 737992773619777599744, 35077254665501330210628, 1762671472887447792620032

Offset

0,3

Links

Table of n, a(n) for n=0..19.

N. J. A. Sloane, Transforms

Formula

a(n) ~ arcsinh(1) * n^n = log(1 + sqrt(2)) * n^n. - Vaclav Kotesovec, Jun 09 2019

Mathematica

Table[n! SeriesCoefficient[Exp[n x] ArcSinh[x], {x, 0, n}], {n, 0, 19}]

Crossrefs

Cf. A001818, A002866, A291483, A302583, A302584, A302585, A302586, A302587, A302605, A302608, A302609.

Sequence in context: A317339 A304338 A115416 * A052577 A203935 A210912

Adjacent sequences: A302603 A302604 A302605 * A302607 A302608 A302609

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 10 2018

Status

approved