A319935 T(n,k) = [x^n] JacobiTheta3(0,x)^k, for 0 <= k <= n, triangle read by rows.

1, 0, 2, 0, 0, 4, 0, 0, 0, 8, 0, 2, 4, 6, 24, 0, 0, 8, 24, 48, 112, 0, 0, 0, 24, 96, 240, 544, 0, 0, 0, 0, 64, 320, 960, 2368, 0, 0, 4, 12, 24, 200, 1020, 3444, 9328, 0, 2, 4, 30, 104, 250, 876, 3542, 12112, 34802, 0, 8, 24, 144, 560, 1560, 4424, 14112, 44640, 129064, 339064

Offset

0,3

Links

Table of n, a(n) for n=0..65.

Example

Triangle starts:
[0] 1
[1] 0, 2
[2] 0, 0, 4
[3] 0, 0, 0,  8
[4] 0, 2, 4,  6,  24
[5] 0, 0, 8, 24,  48, 112
[6] 0, 0, 0, 24,  96, 240,  544
[7] 0, 0, 0,  0,  64, 320,  960, 2368
[8] 0, 0, 4, 12,  24, 200, 1020, 3444,  9328
[9] 0, 2, 4, 30, 104, 250,  876, 3542, 12112, 34802

Maple

A319935row := proc(n) local ser;
ser := j -> series(JacobiTheta3(0, x)^j, x, n+1);
seq(coeff(ser(j), x, n), j=0..n) end:
seq(A319935row(n), n=0..10);

Crossrefs

T(n,n) = A066535(n), row sums A320025.

Cf. A319574, A319934.

Sequence in context: A074644 A321256 A130123 * A136337 A028601 A077958

Adjacent sequences: A319932 A319933 A319934 * A319936 A319937 A319938

Keyword

nonn,tabl

Author

Peter Luschny, Oct 06 2018

Status

approved