A357911 Expansion of Product_{k>=0} (1 - x^(11*k+1)) in powers of x.

1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3, -3, 1, 0, 0, 0, 0, 0, 0, 0, -1, 4, -4, 1, 0, 0, 0

Offset: 0

Author

Seiichi Manyama, Jan 17 2023

Keywords

• sign
• look

Links

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

Crossrefs

Cf. Product_{k>=0} (1 - x^(m*k+1)): A081362 (m=2), A284312 (m=3), A284313 (m=4), A284314 (m=5), A284585 (m=6), A284499 (m=7), this sequence (m=11).

Cf. A357912.

Programs

PARI

my(N=100, x='x+O('x^N)); Vec(prod(k=0, N, 1-x^(11*k+1)))

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, sumdiv(j, d, (Mod(d, 11)==1)*d)*v[i-j+1])/i); v;

Formula

a(0) = 1; a(n) = -(1/n) * Sum_{k=1..n} A357912(k) * a(n-k).