OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Bell Polynomial.
FORMULA
a(n) = Sum_{k=0..n} 9^(n-k) * |Stirling1(n,k)| * A004212(k) = 9^n * Sum_{k=0..n} (1/3)^k * |Stirling1(n,k)| * Bell_k(1/3), where Bell_n(x) is n-th Bell polynomial.
From Vaclav Kotesovec, Aug 02 2024: (Start)
a(n) = 36*(n-2)*a(n-1) - 18*(27*n^2 - 135*n + 172)*a(n-2) + (2916*n^3 - 26244*n^2 + 79056*n - 79703)*a(n-3) - 729*(n-4)*(n-3)*(3*n - 11)*(3*n - 10)*a(n-4).
a(n) ~ 3^(2*n - 1/4) * n^(n - 3/8) / (2*exp(n - 4*n^(1/4)/3^(3/2) + 1/3)) * (1 - 35/(32*sqrt(3)*n^(1/4))). (End)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((1/(1-9*x)^(1/3)-1)/3)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 02 2024
STATUS
approved