login
A375688
Expansion of e.g.f. 1 / (1 + 3 * x * log(1 - x))^(1/3).
2
1, 0, 2, 3, 56, 270, 4824, 44520, 866816, 12195792, 267873120, 5073187680, 126754229568, 2999710359360, 85061489235072, 2400155295632640, 76724104598031360, 2502434971473937920, 89428428468644493312, 3300036525511418327040
OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} (Product_{j=0..k-1} (3*j+1)) * |Stirling1(n-k,k)|/(n-k)!.
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*x*log(1-x))^(1/3)))
(PARI) a(n) = n!*sum(k=0, n\2, prod(j=0, k-1, 3*j+1)*abs(stirling(n-k, k, 1))/(n-k)!);
CROSSREFS
Cf. A347015.
Sequence in context: A041709 A361095 A362835 * A371140 A371121 A371227
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 24 2024
STATUS
approved