A309173 Expansion of Product_{k>=1} (1 + (1 + x + x^2) * x^k).

1, 1, 2, 4, 6, 10, 15, 23, 34, 50, 71, 100, 140, 195, 268, 363, 487, 650, 865, 1145, 1505, 1962, 2541, 3275, 4208, 5390, 6879, 8740, 11053, 13917, 17459, 21837, 27244, 33906, 42085, 52085, 64268, 79071, 97025, 118772, 145082, 176869, 215204, 261333, 316705, 383019

Offset

0,3

Links

Table of n, a(n) for n=0..45.

Formula

G.f.: exp(Sum_{k>=1} x^k * Sum_{d|k} (-1)^(d+1) * (1 + x + x^2)^d/d).

Mathematica

nmax = 45; CoefficientList[Series[Product[(1 + (1 + x + x^2) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 45; CoefficientList[Series[Exp[Sum[x^k Sum[(-1)^(d + 1) (1 + x + x^2)^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x]

Crossrefs

Cf. A160571, A227681, A309172.

Sequence in context: A239288 A306145 A143184 * A116084 A108925 A279026

Adjacent sequences: A309170 A309171 A309172 * A309174 A309175 A309176

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 15 2019

Status

approved