A393559 Expansion of Product_{i>=1, j>=0} (1 + x^(i * 7^j)) / (1 - x^(i * 7^j)).

1, 2, 4, 8, 14, 24, 40, 66, 104, 162, 248, 372, 552, 808, 1172, 1680, 2386, 3360, 4692, 6504, 8952, 12248, 16648, 22500, 30248, 40450, 53832, 71312, 94062, 123540, 161616, 210624, 273484, 353872, 456352, 586632, 751758, 960500, 1223688, 1554672, 1969912, 2489616

Offset

0,2

Comments

Convolution of A373221 and A373298.

In general, for m > 1, if g.f. = Product_{i>=1, j>=0} (1 + x^(i * m^j)) / (1 - x^(i * m^j)), then log(a(n)) ~ Pi*sqrt(m*n/(m-1)).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

log(a(n)) ~ Pi*sqrt(7*n/6).

Mathematica

nmax = 50; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^(IntegerExponent[k, 7] + 1), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 50; CoefficientList[Series[Product[(1+x^(i*7^j))/(1-x^(i*7^j)), {i, 1, nmax}, {j, 0, Log[nmax]/Log[7]+1}], {x, 0, nmax}], x]

Crossrefs

Cf. A327727, A393555, A393556, A393557, A393558.

Cf. A373221, A373298.

Sequence in context: A208605 A123655 A084683 * A271493 A118544 A222037

Adjacent sequences: A393556 A393557 A393558 * A393560 A393561 A393562

Keyword

nonn

Author

Vaclav Kotesovec, Feb 21 2026

Status

approved