A373298 Euler transform of A373217.

1, 1, 2, 3, 5, 7, 11, 16, 23, 32, 45, 61, 84, 112, 152, 200, 265, 345, 451, 581, 750, 960, 1225, 1552, 1965, 2470, 3101, 3872, 4830, 5990, 7421, 9152, 11270, 13825, 16932, 20672, 25191, 30608, 37129, 44920, 54257, 65376, 78660, 94419, 113172, 135370, 161687, 192752

Offset

0,3

Comments

In general, for m > 1, if g.f. = Product_{i>=1, j>=0} 1/(1 - x^(i * m^j)), then log(a(n)) ~ Pi*sqrt(2*m*n/(3*(m-1))). - Vaclav Kotesovec, Feb 21 2026

Links

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

Formula

G.f.: A(x) = 1/Product_{i>=1, j>=0} (1 - x^(i * 7^j)).

Let A(x) be the g.f. of this sequence, and P(x) be the g.f. of A000041, then P(x) = A(x)/A(x^7).

log(a(n)) ~ Pi*sqrt(7*n)/3. - Vaclav Kotesovec, Feb 21 2026

Mathematica

nmax = 60; CoefficientList[1/Series[Product[(1 - x^k)^(IntegerExponent[k, 7] + 1), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 21 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec(1/prod(k=1, N, (1-x^k)^(valuation(k, 7)+1)))

Crossrefs

Cf. A092119, A173241, A373295, A373296, A373297.

Cf. A000041, A373217, A373221.

Sequence in context: A308927 A366850 A024791 * A178240 A118084 A232481

Adjacent sequences: A373295 A373296 A373297 * A373299 A373300 A373301

Keyword

nonn

Author

Seiichi Manyama, May 31 2024

Status

approved