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A292784 a(n) = n! * [x^n] 1/sqrt(1 - 2*n*x). 1
1, 1, 12, 405, 26880, 2953125, 484989120, 111289483305, 34007836262400, 13350287284158825, 6547290750000000000, 3922838769902739011325, 2819575386162274605465600, 2394486245934541921935898125, 2371947271643716575046318080000, 2710687260280640086154937744140625, 3539907755812512418187309922385920000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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}]]

CROSSREFS

Main diagonal of A292783.

Cf. A000312, A001147, A061711, A291699.

Sequence in context: A276482 A202788 A285028 * A003772 A211078 A299382

Adjacent sequences: A292781 A292782 A292783 * A292785 A292786 A292787

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 23 2017

STATUS

approved

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Last modified February 3 20:51 EST 2023. Contains 360045 sequences. (Running on oeis4.)