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A264686 Expansion of Product_{k>=1} (1 + 2*x^k)/(1 - x^k). 5
1, 3, 6, 15, 27, 51, 93, 159, 264, 432, 696, 1086, 1683, 2553, 3837, 5700, 8367, 12147, 17505, 24972, 35361, 49728, 69402, 96243, 132657, 181782, 247692, 335838, 453042, 608289, 813102, 1082256, 1434519, 1894215, 2491644, 3265869, 4265973, 5553771, 7207167 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of A000041 and A032302.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

FORMULA

a(n) ~ sqrt(c) * exp(sqrt(2*c*n)) / (4*Pi*sqrt(3)*n), where c = 2*Pi^2/3 + log(2)^2 + 2*polylog(2, -1/2) = 6.163360867463814765670634381079217086937812673723341... . - Vaclav Kotesovec, Jan 04 2016

MAPLE

b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,

      `if`(n=0, 1, b(n, i-1)+`if`(i>n, 0, 2*b(n-i, i-1))))

    end:

a:= n-> add(b(i$2)*combinat[numbpart](n-i), i=0..n):

seq(a(n), n=0..60);  # Alois P. Heinz, Dec 22 2017

MATHEMATICA

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

PROG

(PARI) { my(n=40); Vec(prod(k=1, n, 3/(1-x^k) - 2 + O(x*x^n))) } \\ Andrew Howroyd, Dec 22 2017

CROSSREFS

Cf. A000041, A006951, A015128, A032302, A261584, A264685, A266821.

Column k=3 of A321884.

Sequence in context: A281420 A280839 A134774 * A165729 A056278 A000740

Adjacent sequences:  A264683 A264684 A264685 * A264687 A264688 A264689

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Nov 21 2015

STATUS

approved

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Last modified July 13 06:22 EDT 2020. Contains 335675 sequences. (Running on oeis4.)