A320025 -id:A320025 - cp's OEIS frontend

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

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Peter Luschny, Oct 06 2018

nonn
tabl

			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

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

Cf. A319574, A319934.

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);

cp's OEIS Frontend

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

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