A292798 a(n) = [x^n] 1/(1 - x - n*x/(1 - x - n*x/(1 - x - n*x/(1 - x - n*x/(1 - x - n*x/(1 - ...)))))), a continued fraction.

1, 2, 15, 244, 6345, 229326, 10663471, 607693640, 41058670113, 3210853971610, 285387481699551, 28423216247375676, 3136023698489382025, 379743303818657805222, 50074394496591697023135, 7143088376895580682492176, 1096075604718147681983312001, 180030794404631168482202007090

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) ~ exp(1/2) * 2^(2*n) * n^(n-3/2) / sqrt(Pi). - Vaclav Kotesovec, Sep 24 2017

a(n) = (1/(n+1)) * [x^n] (1+x)^(n+1) / (1 - n*x)^(n+1). - Paul D. Hanna, May 07 2018

Mathematica

Table[SeriesCoefficient[1/(1 - x + ContinuedFractionK[-n x, 1 - x, {i, 1, n}]), {x, 0, n}], {n, 0, 17}]
Table[SeriesCoefficient[(1 - x + Sqrt[1 - 2 (2 n + 1) x + x^2])/(1 - 2 (n + 1) x + x^2 - (x - 1) Sqrt[1 - 2 (2 n + 1) x + x^2]), {x, 0, n}], {n, 0, 17}]
Table[Hypergeometric2F1[-n, n + 1, 2, -n], {n, 0, 17}]

Prog

(PARI) {a(n) = polcoeff( (1+x)^(n+1) / (1 - n*x +x*O(x^n) )^(n+1), n) / (n+1)}
for(n=0, 30, print1(a(n), ", ")) \\ Paul D. Hanna, May 07 2018

Crossrefs

Main diagonal of A103209 (with offset 0).

Cf. A006318.

Sequence in context: A227098 A180610 A156750 * A221100 A203310 A102555

Adjacent sequences: A292795 A292796 A292797 * A292799 A292800 A292801

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 23 2017

Status

approved