A341364 Expansion of (1 / theta_4(x) - 1)^3 / 8.

1, 6, 24, 77, 216, 552, 1315, 2964, 6387, 13255, 26640, 52074, 99336, 185430, 339483, 610709, 1081227, 1886484, 3247502, 5521365, 9279624, 15429149, 25397088, 41412030, 66928700, 107265576, 170556654, 269164346, 421765920, 656419080, 1015044526, 1559950185, 2383284894

Offset

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..10000

Formula

G.f.: (1/8) * (-1 + Product_{k>=1} (1 + x^k) / (1 - x^k))^3.

a(n) ~ A319552(n)/8 ~ 3*exp(Pi*sqrt(3*n)) / (512*n^(3/2)). - Vaclav Kotesovec, Feb 20 2021

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, 3):
seq(a(n), n=3..35);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 35; CoefficientList[Series[(1/EllipticTheta[4, 0, x] - 1)^3/8, {x, 0, nmax}], x] // Drop[#, 3] &
nmax = 35; CoefficientList[Series[(1/8) (-1 + Product[(1 + x^k)/(1 - x^k), {k, 1, nmax}])^3, {x, 0, nmax}], x] // Drop[#, 3] &

Crossrefs

Cf. A002448, A004404, A014968, A015128, A063691, A319552, A327381, A338223, A341221, A341365, A341366, A341367, A341368, A341369, A341370.

Sequence in context: A297713 A225383 A257956 * A080373 A180437 A276179

Adjacent sequences: A341361 A341362 A341363 * A341365 A341366 A341367

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 10 2021

Status

approved