A367371 Expansion of the e.g.f. (exp(x) / (3 - 2*exp(x)))^(2/3).

1, 2, 8, 52, 468, 5372, 74948, 1230812, 23251908, 496661532, 11834467588, 311195370972, 8950935130948, 279540192840092, 9419760953149828, 340658973061341532, 13160048773006619588, 540850933969855649052, 23561995002376443953668

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * (Product_{j=0..k-1} (3*j+2)) * Stirling2(n,k).

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

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

Prog

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*prod(j=0, k-1, 3*j+2)*stirling(n, k, 2));

Crossrefs

Cf. A136727, A201339.

Cf. A365558.

Sequence in context: A368453 A007832 A111088 * A006351 A300697 A277499

Adjacent sequences: A367368 A367369 A367370 * A367372 A367373 A367374

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2023

Status

approved