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 A306518 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of Product_{d|k} theta_3(q^d). 0
 1, 1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 2, 0, 4, 2, 1, 2, 2, 2, 2, 0, 1, 2, 0, 4, 6, 0, 0, 1, 2, 2, 0, 4, 0, 4, 0, 1, 2, 0, 6, 2, 4, 0, 0, 0, 1, 2, 2, 0, 6, 2, 8, 4, 2, 2, 1, 2, 0, 4, 2, 4, 4, 8, 0, 6, 0, 1, 2, 2, 2, 4, 0, 14, 0, 6, 2, 0, 0, 1, 2, 0, 4, 6, 4, 0, 8, 0, 6, 0, 4, 0, 1, 2, 2, 0, 2, 0, 8, 2, 6, 6, 8, 0, 4, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Eric Weisstein's World of Mathematics, Jacobi Theta Functions FORMULA G.f. of column k: Product_{d|k} theta_3(q^d). EXAMPLE Square array begins: 1, 1, 1, 1, 1, 1, ... 2, 2, 2, 2, 2, 2, ... 0, 2, 0, 2, 0, 2, ... 0, 4, 2, 4, 0, 6, ... 2, 2, 6, 4, 2, 6, ... 0, 0, 0, 4, 2, 4, ... MATHEMATICA Table[Function[k, SeriesCoefficient[Product[EllipticTheta[3, 0, q^d], {d, Divisors[k]}], {q, 0, n}]][i - n + 1], {i, 0, 13}, {n, 0, i}] // Flatten CROSSREFS Columns k=1..48 give A000122, A033715, A033716, A033717, A033718, A033712, A033719, A033720, A033721, A033722, A033723, A033724, A033725, A033726, A033727, A033728, A033729, A033730, A033731, A033732, A033733, A033734, A033735, A033736, A033737, A033738, A033739, A033740, A033741, A033742, A033743, A033744, A033745, A033746, A033747, A033748, A033749, A033750, A033751, A033752, A033753, A033754, A033755, A033756, A033757, A033758, A033759, A033760. Cf. A320305 (diagonal). Sequence in context: A115628 A114002 A114004 * A333310 A049986 A218797 Adjacent sequences: A306515 A306516 A306517 * A306519 A306520 A306521 KEYWORD nonn,tabl AUTHOR Ilya Gutkovskiy, Feb 21 2019 STATUS approved

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Last modified March 24 02:50 EDT 2023. Contains 361454 sequences. (Running on oeis4.)