login
A302606
a(n) = n! * [x^n] exp(n*x)*arcsinh(x).
3
0, 1, 4, 26, 240, 2884, 42660, 748544, 15185856, 349574544, 9000902500, 256293989984, 7996078704240, 271246034903232, 9939835626507332, 391303051339622400, 16469438021801262848, 737992773619777599744, 35077254665501330210628, 1762671472887447792620032
OFFSET
0,3
LINKS
FORMULA
a(n) ~ arcsinh(1) * n^n = log(1 + sqrt(2)) * n^n. - Vaclav Kotesovec, Jun 09 2019
a(n) = Sum_{k=1..n, k odd} (-1)^((k-1)/2)*binomial(n,k)*(k-2)!!^2*n^(n-k). - Fabian Pereyra, Oct 05 2024
MATHEMATICA
Table[n! SeriesCoefficient[Exp[n x] ArcSinh[x], {x, 0, n}], {n, 0, 19}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 10 2018
STATUS
approved