A341367 Expansion of (1 / theta_4(x) - 1)^6 / 64.

1, 12, 84, 442, 1932, 7392, 25551, 81468, 243126, 686400, 1848156, 4775874, 11904215, 28737732, 67416756, 154122912, 344177823, 752310720, 1612395007, 3393652848, 7023685794, 14311193104, 28737793986, 56924936052, 111323290934, 215095157964, 410895944148, 776529566516

Offset

6,2

Links

Table of n, a(n) for n=6..33.

Formula

G.f.: (1/64) * (-1 + Product_{k>=1} (1 + x^k) / (1 - x^k))^6.

Maple

g:= proc(n, i) option remember; `if`(n=0, 1/2, `if`(i=1, 0,
      g(n, i-1))+add(2*g(n-i*j, i-1), j=`if`(i=1, n, 1)..n/i))
    end:
b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0,
      g(n$2)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
    end:
a:= n-> b(n, 6):
seq(a(n), n=6..33);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 33; CoefficientList[Series[(1/EllipticTheta[4, 0, x] - 1)^6/64, {x, 0, nmax}], x] // Drop[#, 6] &
nmax = 33; CoefficientList[Series[(1/64) (-1 + Product[(1 + x^k)/(1 - x^k), {k, 1, nmax}])^6, {x, 0, nmax}], x] // Drop[#, 6] &

Crossrefs

Cf. A002448, A004407, A014968, A015128, A327384, A338223, A340905, A341225, A341364, A341365, A341366, A341368, A341369, A341370.

Sequence in context: A085409 A303916 A111464 * A004407 A054849 A000761

Adjacent sequences: A341364 A341365 A341366 * A341368 A341369 A341370

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 10 2021

Status

approved