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A367371
Expansion of the e.g.f. (exp(x) / (3 - 2*exp(x)))^(2/3).
0
1, 2, 8, 52, 468, 5372, 74948, 1230812, 23251908, 496661532, 11834467588, 311195370972, 8950935130948, 279540192840092, 9419760953149828, 340658973061341532, 13160048773006619588, 540850933969855649052, 23561995002376443953668
OFFSET
0,2
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. A365558.
Sequence in context: A368453 A007832 A111088 * A006351 A300697 A277499
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 15 2023
STATUS
approved