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 A321179 a(n) = [x^(n^2)] Product_{k=1..n} theta_3(q^k), where theta_3() is the Jacobi theta function. 1
 1, 2, 2, 14, 44, 174, 988, 4314, 20780, 126320, 692328, 3836166, 23160914, 135752866, 803203484, 4902966108, 29745996950, 181712320506, 1124481497694, 6965802854354, 43360326335154, 271658784580760, 1706393926177980, 10757142052998054, 68081390206251952, 432001821971576352 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also the number of integer solutions (a_1, a_2, ... , a_n) to the equation a_1^2 + 2*a_2^2 + ... + n*a_n^2 = n^2. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..400 (first 91 terms from Seiichi Manyama) FORMULA a(n) ~ c * d^n / n^(7/4), where d = 6.8137220913147... and c = 0.178176349247... - Vaclav Kotesovec, Oct 30 2018 EXAMPLE Solutions (a_1, a_2, a_3) to the equation a_1^2 + 2*a_2^2 + 3*a_3^2 = 9. ------------------------------------------------------------------------ ( 1, 2, 0), ( 1, -2, 0), (-1, 2, 0), (-1, -2, 0), ( 2, 1, 1), ( 2, 1, -1), ( 2, -1, 1), ( 2, -1, -1), (-2, 1, 1), (-2, 1, -1), (-2, -1, 1), (-2, -1, -1), ( 3, 0, 0), (-3, 0, 0). MATHEMATICA nmax = 20; Table[SeriesCoefficient[Product[EllipticTheta[3, 0, x^k], {k, 1, n}], {x, 0, n^2}], {n, 0, nmax}] (* Vaclav Kotesovec, Oct 29 2018 *) PROG (PARI) {a(n) = polcoeff(prod(i=1, n, 1+2*sum(j=1, sqrtint(n^2\i), x^(i*j^2)+x*O(x^(n^2)))), n^2)} CROSSREFS Cf. A000122, A000290, A320067, A320931, A321139. Sequence in context: A264508 A194689 A277556 * A345370 A166114 A202730 Adjacent sequences: A321176 A321177 A321178 * A321180 A321181 A321182 KEYWORD nonn AUTHOR Seiichi Manyama, Oct 29 2018 STATUS approved

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Last modified June 4 09:09 EDT 2023. Contains 363121 sequences. (Running on oeis4.)