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A088369 Expansion of e.g.f.: 1/(1-x-x^2)^x. 1
1, 0, 2, 9, 44, 390, 3474, 37800, 471344, 6602904, 103271400, 1779944760, 33542915592, 686101244400, 15139184749584, 358465510133640, 9066087526045440, 243928110816129600, 6956913949298380224, 209651038286581756800, 6656701196017929467520, 222116657005058778103680 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) ~ n! * n^(c-1) / (Gamma(c) * 5^(c/2) * c^c * c^n), where c = (sqrt(5)-1)/2. - Vaclav Kotesovec, Nov 05 2014
MATHEMATICA
With[{nn=30}, CoefficientList[Series[1/(1-x-x^2)^x, {x, 0, nn}], x]Range[ 0, nn]!] (* Harvey P. Dale, May 06 2012 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( 1/(1-x-x^2)^x ))); // G. C. Greubel, Dec 12 2022
(SageMath)
def A088369_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( exp(-x*log(1-x-x^2)) ).egf_to_ogf().list()
A088369_list(40) # G. C. Greubel, Dec 12 2022
(PARI) my(x='x+O('x^22)); Vec(serlaplace(1/(1-x-x^2)^x)) \\ Joerg Arndt, Dec 13 2022
CROSSREFS
Sequence in context: A318913 A327940 A354623 * A356588 A303938 A059388
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 28 2003
EXTENSIONS
Definition corrected by Vaclav Kotesovec, Nov 05 2014
STATUS
approved

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Last modified December 2 06:18 EST 2023. Contains 367509 sequences. (Running on oeis4.)