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A280225 G.f.: Product_{k>=1} (1 + 3*x^(k^2)) / (1-x^k). 3
1, 4, 5, 9, 17, 34, 47, 75, 109, 165, 240, 341, 473, 671, 936, 1268, 1722, 2325, 3091, 4099, 5403, 7083, 9207, 11923, 15339, 19682, 25134, 31909, 40378, 50954, 64068, 80171, 100089, 124506, 154465, 191043, 235636, 289816, 355673, 435285, 531486, 647478 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of A279368 and A000041.

In general, if m >= 0 and g.f. = Product_{k>=1} (1 + m*x^(k^2)) / (1-x^k), then a(n) ~ exp(Pi*sqrt((2*n)/3) + 3^(1/4)*c*n^(1/4)/ 2^(3/4) - 3*c^2/(32*Pi)) / (4*sqrt(3)*sqrt(m+1)*n), where c = -PolyLog(3/2, -m).

LINKS

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

FORMULA

a(n) ~ exp(Pi*sqrt((2*n)/3) + 3^(1/4)*c*n^(1/4)/ 2^(3/4) - 3*c^2/(32*Pi)) / (8*sqrt(3)*n), where c = -PolyLog(3/2, -3).

MATHEMATICA

nmax=50; CoefficientList[Series[Product[(1+3*x^(k^2))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000041, A033461, A279368, A280204, A280224.

Sequence in context: A255978 A069089 A143096 * A153058 A216225 A276645

Adjacent sequences:  A280222 A280223 A280224 * A280226 A280227 A280228

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Dec 29 2016

STATUS

approved

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Last modified January 17 09:52 EST 2020. Contains 330949 sequences. (Running on oeis4.)