A305460 a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) + 2*a(n-2).

1, 3, 20, 186, 2272, 34452, 624680, 13187184, 317741776, 8605402320, 258797553152, 8557530058656, 308588677217920, 12052073471616192, 506804263162315904, 22830295989247448064, 1096867816010202138880, 55985919208498803979008

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)*2^k.

a(n) ~ BesselI(0, 2*sqrt(2)/3) * n! * 3^n. - Vaclav Kotesovec, Jun 03 2018

Maple

a:=proc(n) option remember: if n=0 then 1 elif n=1 then 3 elif n>=2 then 3*n*procname(n-1)+2*procname(n-2) fi; end:
seq(a(n), n=0..20); # Muniru A Asiru, Jun 01 2018

Prog

(PARI) {a(n) = sum(k=0, n/2, ((n-k)!/k!)*binomial(n-k, k)*3^(n-2*k)*2^k)}
(GAP) List([0..20], n->Sum([0..Int(n/2)], k->((Factorial(n-k))/(Factorial(k))*Binomial(n-k, k)*3^(n-2*k)*2^k))); # Muniru A Asiru, Jun 01 2018

Crossrefs

Cf. A222467, A305459.

Sequence in context: A212789 A065980 A302581 * A073767 A226349 A208975

Adjacent sequences: A305457 A305458 A305459 * A305461 A305462 A305463

Keyword

nonn

Author

Seiichi Manyama, Jun 01 2018

Status

approved