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

%I A319935 #6 Oct 07 2018 04:38:11
%S A319935 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,
%T A319935 0,0,0,64,320,960,2368,0,0,4,12,24,200,1020,3444,9328,0,2,4,30,104,
%U A319935 250,876,3542,12112,34802,0,8,24,144,560,1560,4424,14112,44640,129064,339064
%N A319935 T(n,k) = [x^n] JacobiTheta3(0,x)^k, for 0 <= k <= n, triangle read by rows.
%e A319935 Triangle starts:
%e A319935 [0] 1
%e A319935 [1] 0, 2
%e A319935 [2] 0, 0, 4
%e A319935 [3] 0, 0, 0,  8
%e A319935 [4] 0, 2, 4,  6,  24
%e A319935 [5] 0, 0, 8, 24,  48, 112
%e A319935 [6] 0, 0, 0, 24,  96, 240,  544
%e A319935 [7] 0, 0, 0,  0,  64, 320,  960, 2368
%e A319935 [8] 0, 0, 4, 12,  24, 200, 1020, 3444,  9328
%e A319935 [9] 0, 2, 4, 30, 104, 250,  876, 3542, 12112, 34802
%p A319935 A319935row := proc(n) local ser;
%p A319935 ser := j -> series(JacobiTheta3(0, x)^j, x, n+1);
%p A319935 seq(coeff(ser(j), x, n), j=0..n) end:
%p A319935 seq(A319935row(n), n=0..10);
%Y A319935 T(n,n) = A066535(n), row sums A320025.
%Y A319935 Cf. A319574, A319934.
%K A319935 nonn,tabl
%O A319935 0,3
%A A319935 _Peter Luschny_, Oct 06 2018