A302583 a(n) = ((n + 1)^n - (n - 1)^n)/2.

0, 1, 4, 28, 272, 3376, 51012, 908608, 18640960, 432891136, 11225320100, 321504185344, 10079828372880, 343360783937536, 12627774819845668, 498676704524517376, 21046391759976988928, 945381827279671853056, 45032132922921758270916, 2267322327322331161821184

Offset: 0

Author

Ilya Gutkovskiy, Apr 10 2018

Keywords

• nonn

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000169, A065440, A007778, A062024, A115416, A274278, A293022, A302584, A302585, A302586, A302587.

Programs

Mathematica

Table[((n + 1)^n - (n - 1)^n)/2, {n, 0, 19}]
nmax = 19; CoefficientList[Series[(x^2 - LambertW[-x]^2)/(2 x LambertW[-x] (1 + LambertW[-x])), {x, 0, nmax}], x] Range[0, nmax]!
Table[n! SeriesCoefficient[Exp[n x] Sinh[x], {x, 0, n}], {n, 0, 19}]

Formula

E.g.f.: (x^2 - LambertW(-x)^2)/(2*x*LambertW(-x)*(1 + LambertW(-x))).

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