A392779 Number of distinct coefficients in the expansion of x_1(x_1 + x_2)...(x_1 + x_2 + ... + x_n).

1, 1, 1, 2, 4, 7, 14, 29, 56, 109, 207, 369, 629, 1063, 1825, 3194, 5700, 10172, 17822, 30540, 51442, 85836, 142809, 237876, 396590, 660032, 1093409, 1800392, 2944809, 4782820, 7709207, 12322508, 19517477, 30622829

Offset

0,4

Links

Table of n, a(n) for n=0..33.

Example

x_1(x_1 + x_2)(x_1 + x_2 + x_3) = x_1^3 + 2*x_1^2x_2 + x_1x_2^2 + x_1^2x_3 + x_1x_2x_3, so the distinct coefficients are 1 and 2. Therefore, a(3) = 2.

Prog

(Python)
from math import prod
from sympy import symbols, Poly
def A392779(n):
    if n == 0: return 1
    s = symbols('x_0:'+str(n))
    return len(set(Poly(prod(sum(s[j] for j in range(i)) for i in range(1, n+1))).coeffs())) # Chai Wah Wu, Mar 30 2026

Crossrefs

Cf. A000108, A347917, A349404.

Sequence in context: A119342 A119268 A002989 * A293336 A321401 A000671

Adjacent sequences: A392776 A392777 A392778 * A392780 A392781 A392782

Keyword

nonn,more

Author

Seiichi Manyama, Mar 30 2026

Status

approved