A302608 a(n) = n! * [x^n] exp(n*x)*arctan(x).

0, 1, 4, 25, 224, 2649, 38880, 679449, 13749248, 315919665, 8122432000, 231002307449, 7199799644160, 244028744225993, 8936047251296256, 351569799174274425, 14789182545666244608, 662389019735008588129, 31470659616611382460416, 1580849762199983023572313

Offset: 0

Author

Ilya Gutkovskiy, Apr 10 2018

Keywords

• nonn

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A010050, A279927, A293192, A302583, A302584, A302585, A302586, A302587, A302605, A302606, A302609.

Programs

Mathematica

Table[n! SeriesCoefficient[Exp[n x] ArcTan[x], {x, 0, n}], {n, 0, 19}]
Join[{0}, Table[n^n (HypergeometricPFQ[{1, 1, 1 - n}, {2}, -(I/n)] + HypergeometricPFQ[{1, 1, 1 - n}, {2}, I/n])/2, {n, 19}]]

Formula

a(n) ~ arctan(1) * n^n. - Vaclav Kotesovec, Jun 09 2019

a(n) = Sum_{k=1..n, k odd} (-1)^((k-1)/2)*binomial(n,k)*(k-1)!*n^(n-k). - Fabian Pereyra, Oct 05 2024