A293022 -id:A293022 - cp's OEIS frontend

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

Ilya Gutkovskiy, Apr 10 2018

nonn

N. J. A. Sloane, Transforms

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

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}]

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).

A292966 a(n) = (2n)! [x^(2n)] exp(n(cosh(x)-1)).

Original entry on oeis.org

1, 1, 14, 543, 41332, 5203880, 979067634, 257327195587, 90055440034760, 40484356990454979, 22735298894247204310, 15597865046044378254146, 12836943134715746781979644, 12482280872844033169540407253, 14157380505669130674125989779482, 18524549200247005824873100782063015

Offset: 0

Ilya Gutkovskiy, Sep 29 2017

nonn

Cf. A005046, A293022.

Table[(2 n)! SeriesCoefficient[Exp[n (Cosh[x] - 1)], {x, 0, 2 n}], {n, 0, 15}]
Table[(-1)^n (2 n)! SeriesCoefficient[Exp[n (Cos[x] - 1)], {x, 0, 2 n}], {n, 0, 15}]

cp's OEIS Frontend

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

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Formula

A292966 a(n) = (2n)! [x^(2n)] exp(n(cosh(x)-1)).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A292966 a(n) = (2*n)! * [x^(2*n)] exp(n*(cosh(x)-1)).

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Author

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Crossrefs

Programs

Mathematica

A292966 a(n) = (2n)! [x^(2n)] exp(n(cosh(x)-1)).