

A014809


Expansion of Jacobi theta constant (theta_2/2)^24.


15



1, 24, 276, 2048, 11178, 48576, 177400, 565248, 1612875, 4200352, 10131156, 22892544, 48897678, 99448320, 193740408, 363315200, 658523925, 1157743824, 1980143600, 3303168000, 5386270686, 8602175744, 13477895856, 20748607488, 31425764410, 46883528256, 68969957700
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OFFSET

0,2


COMMENTS

Number of ways of writing n as the sum of 24 triangular numbers from A000217.


LINKS



FORMULA

G.f.: 24th power of the g.f. for A010054.
a(n) = (A096963(n+3)  tau(n+3)  2072*tau((n+3)/2))/176896, with Ramanujan's tau function given in A000594, and tau(n) is put to 0 if n is not integer. See the Ono et al. link, case k=24, Theorem 8.
(End)
a(n) = 1/72 * Sum_{a, b, x, y > 0, a*x + b*y = n + 3, x == y == 1 mod 2 and a > b} (a*b)^3*(a^2  b^2)^2.  Seiichi Manyama, May 05 2017


CROSSREFS

Number of ways of writing n as a sum of k triangular numbers, for k=1,...: A010054, A008441, A008443, A008438, A008439, A008440, A226252, A007331, A226253, A226254, A226255, A014787, A014809.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



