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A261031 Euler transform of Lucas numbers. 5
1, 1, 4, 8, 21, 44, 103, 217, 477, 999, 2116, 4373, 9055, 18464, 37576, 75725, 152047, 303158, 602085, 1189242, 2340065, 4584027, 8947865, 17399906, 33725509, 65153150, 125493914, 241011287, 461611911, 881806114, 1680336592, 3194346093, 6058770147, 11466709780 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

FORMULA

a(n) ~ phi^n / (2*sqrt(Pi)*n^(3/4)) * exp(-1 + 1/(2*sqrt(5)) + 2*sqrt(n) + s), where s = Sum_{k>=2} (2 + phi^k)/((phi^(2*k) - phi^k - 1)*k) = 0.9799662013576411396292209835034813778512885279062665867878344706... and phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Aug 07 2015

MAPLE

L:= proc(n) option remember; `if`(n<2, 2-n, L(n-2)+L(n-1)) end:

a:= proc(n) option remember; `if`(n=0, 1, add(add(d*

      L(d), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)

    end:

seq(a(n), n=0..40);  # Alois P. Heinz, Jan 12 2017

MATHEMATICA

CoefficientList[Series[Product[1/(1 - x^k)^LucasL[k], {k, 1, 30}], {x, 0, 30}], x]

CROSSREFS

Cf. A000032, A166861.

Sequence in context: A061256 A180608 A244583 * A077921 A097076 A003608

Adjacent sequences:  A261028 A261029 A261030 * A261032 A261033 A261034

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Aug 07 2015

STATUS

approved

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Last modified February 21 17:43 EST 2018. Contains 299414 sequences. (Running on oeis4.)