A305472 a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) - 2*a(n-2).

1, 3, 16, 138, 1624, 24084, 430264, 8987376, 214836496, 5782610640, 173048646208, 5699040103584, 204819346436608, 7976556430820544, 334605731401589632, 15041304800209892352, 721313418947271653632, 36756901756710434550528

Offset: 0

Author

Seiichi Manyama, Jun 02 2018

Keywords

• nonn

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

Crossrefs

Cf. A305460, A305471.

Programs

PARI

{a(n) = sum(k=0, n/2, ((n-k)!/k!)*binomial(n-k, k)*3^(n-2*k)*(-2)^k)}

Formula

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