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A261331 Expansion of Product_{k>=1} (1+x^k)^(A000129(k)). 4
1, 1, 2, 7, 18, 52, 143, 396, 1083, 2971, 8087, 21981, 59533, 160857, 433467, 1165542, 3126951, 8372451, 22374172, 59684669, 158941356, 422582925, 1121814072, 2973703449, 7871754065, 20809918535, 54943916547, 144891525408, 381647503607, 1004149670985 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Vaclav Kotesovec, Asymptotics of the Euler transform of Fibonacci numbers, arXiv:1508.01796 [math.CO], Aug 07 2015

Eric Weisstein's World of Mathematics, Pell Number

Wikipedia, Pell number

FORMULA

a(n) ~ (1+sqrt(2))^n * exp(-1/8 + 2^(1/4)*sqrt(n) + s) / (2^(11/8) * sqrt(Pi) * n^(3/4)), where s = Sum_{k>=2} (-1)^(k+1)/(((sqrt(2)+1)^k - (sqrt(2)-1)^k - 2)*k) = -0.1149083344289588668149210160138124159112948627968378825745674888...

G.f.: exp(Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - 2*x^k - x^(2*k)))). - Ilya Gutkovskiy, May 30 2018

MATHEMATICA

nmax=40; Pell[0]=0; Pell[1]=1; Pell[n_]:=Pell[n] = 2*Pell[n-1] + Pell[n-2]; CoefficientList[Series[Product[(1+x^k)^Pell[k], {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000129, A261329, A261330, A261332, A261050, A261051.

Sequence in context: A280598 A006869 A099626 * A046672 A046866 A291255

Adjacent sequences:  A261328 A261329 A261330 * A261332 A261333 A261334

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Aug 15 2015

STATUS

approved

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Last modified February 20 17:04 EST 2020. Contains 332080 sequences. (Running on oeis4.)