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

Author

Peter Luschny, Oct 06 2018

Keywords

• nonn
• tabl

Examples

			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
		

Crossrefs

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

Cf. A319574, A319934.

Programs

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);