OFFSET
0,2
FORMULA
a(0) = 1; a(n) = Sum_{k=0..n-1} 3^(n-k) * (n-1+k)! / (2^k * k! * (n-1-k)!).
a(n) = (2*n-3)*a(n-1) + 9*a(n-2).
MAPLE
# The row polynomials of A132062 evaluated at x = 3.
T := proc(n, k) option remember; if k = 0 then 0^n elif n < k then 0
else (2*(n - 1) - k)*T(n - 1, k) + T(n - 1, k - 1) fi end:
seq(add(T(n, k)*3^k, k = 0..n), n = 0..19); # Peter Luschny, Apr 25 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(3*(1-sqrt(1-2*x)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 30 2024
STATUS
approved