A341368 Expansion of (1 / theta_4(x) - 1)^7 / 128.

1, 14, 112, 665, 3248, 13776, 52437, 183080, 595399, 1824109, 5310144, 14787542, 39605363, 102465972, 257005641, 626841236, 1490521109, 3462881324, 7875519169, 17562223791, 38456245849, 82793422502, 175452110162, 366348547908, 754392685046, 1533283745644, 3078157040665

Offset: 7

Author

Ilya Gutkovskiy, Feb 10 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..10000

Crossrefs

Cf. A002448, A004408, A014968, A015128, A327385, A338223, A340906, A341226, A341364, A341365, A341366, A341367, A341369, A341370.

Programs

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, 7):
seq(a(n), n=7..33);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 33; CoefficientList[Series[(1/EllipticTheta[4, 0, x] - 1)^7/128, {x, 0, nmax}], x] // Drop[#, 7] &
nmax = 33; CoefficientList[Series[(1/128) (-1 + Product[(1 + x^k)/(1 - x^k), {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &

Formula

G.f.: (1/128) * (-1 + Product_{k>=1} (1 + x^k) / (1 - x^k))^7.