|
| |
|
|
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
|
Table of n, a(n) for n=0..104.
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
|
| |
|
|
