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A303333 a(n) = [x^n] (theta_3(x^(1/2))^n + theta_4(x^(1/2))^n)/2, where theta_3() and theta_4() are the Jacobi theta functions. 3
1, 0, 4, 24, 24, 560, 2080, 11088, 74864, 343536, 2050344, 11676280, 61903776, 363737712, 2022013760, 11335886864, 65187410400, 365627715968, 2085523894756, 11894205734280, 67517852274384, 386394626371680, 2205027379874400, 12602057718873040, 72195482578935488, 413235574714857360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, p. 118.

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

FORMULA

a(n) = A297331(n,n).

a(n) ~ c * d^n / sqrt(n), where d = 5.84456473064455581274428417... and c = 0.14104739588693592503498... - Vaclav Kotesovec, Jun 26 2019

MATHEMATICA

Table[SeriesCoefficient[(EllipticTheta[3, 0, x^(1/2)]^n + EllipticTheta[4, 0, x^(1/2)]^n)/2, {x, 0, n}], {n, 0, 25}]

Table[SeriesCoefficient[EllipticTheta[3, 0, x]^n, {x, 0, 2 n}], {n, 0, 25}]

Table[SeriesCoefficient[EllipticTheta[3, 0, Sqrt[x]]^n, {x, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Jun 26 2019 *)

CROSSREFS

Main diagonal of A297331.

Cf. A066535.

Sequence in context: A169688 A222595 A103225 * A324517 A137980 A144137

Adjacent sequences:  A303330 A303331 A303332 * A303334 A303335 A303336

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 21 2018

STATUS

approved

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Last modified April 21 17:34 EDT 2021. Contains 343156 sequences. (Running on oeis4.)