A292784 a(n) = n! * [x^n] 1/sqrt(1 - 2*n*x).

1, 1, 12, 405, 26880, 2953125, 484989120, 111289483305, 34007836262400, 13350287284158825, 6547290750000000000, 3922838769902739011325, 2819575386162274605465600, 2394486245934541921935898125, 2371947271643716575046318080000, 2710687260280640086154937744140625, 3539907755812512418187309922385920000

Offset: 0

Author

Ilya Gutkovskiy, Sep 23 2017

Keywords

• nonn

Crossrefs

Main diagonal of A292783.

Cf. A000312, A001147, A061711, A291699.

Programs

Mathematica

Table[n! SeriesCoefficient[1/Sqrt[1 - 2 n x], {x, 0, n}], {n, 0, 16}]
Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-i n x, 1, {i, 1, n}]), {x, 0, n}], {n, 0, 16}]
Join[{1}, Table[n^n (2 n - 1)!!, {n, 1, 16}]]

Formula

a(n) = [x^n] 1/(1 - n*x/(1 - 2*n*x/(1 - 3*n*x/(1 - 4*n*x/(1 - 5*n*x/(1 - ...)))))), a continued fraction.

a(n) = A000312(n)*A001147(n).