OFFSET
1,5
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 antidiagonals)
FORMULA
G.f. of column k: Sum_{j>=1} j^k*x^j/(1 + x^(2*j)).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 2, 4, 8, 16, 32, ...
0, 2, 8, 26, 80, 242, ...
1, 4, 16, 64, 256, 1024, ...
2, 6, 26, 126, 626, 3126, ...
0, 4, 32, 208, 1280, 7744, ...
MATHEMATICA
Table[Function[k, SeriesCoefficient[Sum[j^k x^j/(1 + x^(2 j)), {j, 1, n}], {x, 0, n}]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten
PROG
(PARI) T(n, k)={sumdiv(n, d, if(d%2, (-1)^((d-1)/2)*(n/d)^k))}
for(n=1, 10, for(k=0, 8, print1(T(n, k), ", ")); print); \\ Andrew Howroyd, Nov 26 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Nov 26 2018
STATUS
approved