A323633 Expansion of 1/Sum_{k>=0} x^(k^3).

1, -1, 1, -1, 1, -1, 1, -1, 0, 1, -2, 3, -4, 5, -6, 7, -7, 6, -4, 1, 3, -8, 14, -21, 28, -34, 38, -40, 38, -31, 18, 2, -29, 62, -99, 139, -178, 211, -232, 234, -210, 154, -62, -70, 242, -449, 680, -917, 1135, -1303, 1386, -1344, 1136, -725, 85, 794, -1898, 3183, -4571

Offset: 0

Author

Ilya Gutkovskiy, Jan 21 2019

Keywords

• sign

Comments

Convolution inverse of A010057.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A010057, A023358, A317665.

Programs

Maple

a:=series(1/add(x^(k^3),k=0..100),x=0,59): seq(coeff(a,x,n),n=0..58); # Paolo P. Lava, Apr 02 2019

Mathematica

nmax = 58; CoefficientList[Series[1/Sum[x^k^3, {k, 0, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -Sum[Boole[IntegerQ[k^(1/3)]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 58}]

PARI

my(N=66, x='x+O('x^N)); Vec(1/sum(k=0, N^(1/3), x^k^3)) \\ Seiichi Manyama, Mar 19 2022

PARI

a(n) = if(n==0, 1, -sum(k=1, n, ispower(k, 3)*a(n-k))); \\ Seiichi Manyama, Mar 19 2022

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} A010057(k) * a(n-k). - Seiichi Manyama, Mar 19 2022