A293470 a(n) = [x^n] (1/(1 - x/(1 - 2*x/(1 - 3*x/(1 - 4*x/(1 - 5*x/(1 - 6*x/(1 - ...))))))))^n, a continued fraction.

1, 1, 7, 64, 691, 8506, 117586, 1811902, 30977059, 585159526, 12157511122, 276365651992, 6835179127294, 182885413524568, 5265255383238592, 162296482607602714, 5332203008816278819, 185989603728568482598, 6863252473075010369626, 267102762222709967674384, 10932746393513621360731066

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Index entries for sequences related to factorial numbers

Formula

a(n) ~ 2^(n + 1/2) * n^(n+1) / exp(n - 1/2). - Vaclav Kotesovec, Sep 16 2021

Mathematica

Table[SeriesCoefficient[1/(1 + ContinuedFractionK[-k x, 1, {k, 1, n}])^n, {x, 0, n}], {n, 0, 20}]
Table[SeriesCoefficient[Sum[(2 k - 1)!! x^k, {k, 0, n}]^n, {x, 0, n}], {n, 0, 20}]

Crossrefs

Cf. A001147, A034430, A113551, A287899, A293471.

Sequence in context: A371404 A213515 A349333 * A256506 A008787 A261500

Adjacent sequences: A293467 A293468 A293469 * A293471 A293472 A293473

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 09 2017

Status

approved