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A280451 G.f.: Product_{k>=1, j>=1} (1+x^(j*k^2)). 9
1, 1, 1, 2, 3, 4, 5, 7, 9, 13, 16, 20, 27, 34, 42, 53, 67, 82, 102, 125, 153, 188, 227, 274, 332, 401, 478, 574, 686, 815, 969, 1147, 1356, 1600, 1884, 2210, 2597, 3040, 3547, 4141, 4824, 5607, 6508, 7546, 8732, 10100, 11656, 13431, 15473, 17793, 20429, 23436 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

a(n) ~ exp(Pi^2*sqrt(n/2)/3 + sqrt(3) * (sqrt(2)-1) * Zeta(1/2) * Zeta(3/2) * n^(1/4) / (2^(3/4) * sqrt(Pi)) - 9*((sqrt(2)-1) * Zeta(1/2) * Zeta(3/2))^2 / (16*Pi^3)) * sqrt(Pi) / (2^(3/2) * sqrt(3) * n^(3/4)).

MATHEMATICA

nmax = 100; CoefficientList[Series[Product[(1 + x^(j*k^2)), {k, 1, Floor[Sqrt[nmax]+1]}, {j, 1, Floor[nmax/k^2] + 1}], {x, 0, nmax}], x]

CROSSREFS

Cf. A004101, A006171, A107742, A280663, A280664.

Sequence in context: A117603 A250553 A026450 * A240178 A039863 A036802

Adjacent sequences:  A280448 A280449 A280450 * A280452 A280453 A280454

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jan 03 2017

STATUS

approved

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Last modified February 26 03:24 EST 2020. Contains 332272 sequences. (Running on oeis4.)