OFFSET
10,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 10..10000
FORMULA
G.f.: (1/1024) * (-1 + Product_{k>=1} (1 + x^k) / (1 - x^k))^10.
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, 10):
seq(a(n), n=10..34); # Alois P. Heinz, Feb 10 2021
MATHEMATICA
nmax = 34; CoefficientList[Series[(1/EllipticTheta[4, 0, x] - 1)^10/1024, {x, 0, nmax}], x] // Drop[#, 10] &
nmax = 34; CoefficientList[Series[(1/1024) (-1 + Product[(1 + x^k)/(1 - x^k), {k, 1, nmax}])^10, {x, 0, nmax}], x] // Drop[#, 10] &
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 10 2021
STATUS
approved