OFFSET
0,2
COMMENTS
Let S(i,j,n) denote a sequence of the form a(0) = 1, a(1) = i, a(n) = i*n*a(n-1) + j*a(n-2). Then S(i,j,n) = Sum_{k=0..floor(n/2)} ((n-k)!/k!)*binomial(n-k,k)*i^(n-2*k)*j^k.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..380
FORMULA
a(n) = Sum_{k=0..floor(n/2)} ((n-k)!/k!)*binomial(n-k,k)*3^(n-2*k)*(-1)^k.
a(n) ~ BesselJ(0, 2/3) * n! * 3^n. - Vaclav Kotesovec, Jun 03 2018
PROG
(PARI) {a(n) = sum(k=0, n/2, ((n-k)!/k!)*binomial(n-k, k)*3^(n-2*k)*(-1)^k)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 02 2018
STATUS
approved