A302608 - OEIS

%I #15 Oct 25 2024 10:14:57

%S 0,1,4,25,224,2649,38880,679449,13749248,315919665,8122432000,

%T 231002307449,7199799644160,244028744225993,8936047251296256,

%U 351569799174274425,14789182545666244608,662389019735008588129,31470659616611382460416,1580849762199983023572313

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

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F a(n) ~ arctan(1) * n^n. - _Vaclav Kotesovec_, Jun 09 2019

%F 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

%t Table[n! SeriesCoefficient[Exp[n x] ArcTan[x], {x, 0, n}], {n, 0, 19}]

%t Join[{0}, Table[n^n (HypergeometricPFQ[{1, 1, 1 - n}, {2}, -(I/n)] + HypergeometricPFQ[{1, 1, 1 - n}, {2}, I/n])/2, {n, 19}]]

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

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Apr 10 2018