A382753 Expansion of e.g.f. 3/(5 - 2*exp(3*x)).

1, 2, 14, 138, 1806, 29562, 580734, 13309578, 348611886, 10272416922, 336326121054, 12112707922218, 475894244100366, 20255443904321082, 928448378212678974, 45597074777924954058, 2388608236671667179246, 132947999835258872046042, 7835059049893316949502494

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Wikipedia, Polylogarithm.

Formula

a(n) = (-3)^(n+1)/5 * Li_{-n}(5/2), where Li_{n}(x) is the polylogarithm function.

a(n) = 3^(n+1)/5 * Sum_{k>=0} k^n * (2/5)^k.

a(n) = Sum_{k=0..n} 2^k * 3^(n-k) * k! * Stirling2(n,k).

a(n) = (2/5) * A201367(n) = (2/5) * Sum_{k=0..n} 5^k * (-3)^(n-k) * k! * Stirling2(n,k) for n > 0.

a(0) = 1; a(n) = 2 * Sum_{k=1..n} 3^(k-1) * binomial(n,k) * a(n-k).

a(0) = 1; a(n) = 2 * a(n-1) + 5 * Sum_{k=1..n-1} (-3)^(k-1) * binomial(n-1,k) * a(n-k).

Prog

(PARI) a(n) = (-3)^(n+1)*polylog(-n, 5/2)/5;

Crossrefs

Cf. A094417, A326324, A384435.

Cf. A004123, A216794, A384521.

Cf. A201367.

Sequence in context: A336182 A224729 A355722 * A303395 A301271 A245267

Adjacent sequences: A382750 A382751 A382752 * A382754 A382755 A382756

Keyword

nonn

Author

Seiichi Manyama, Jun 03 2025

Status

approved