A305471 a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) - a(n-2).

1, 3, 17, 150, 1783, 26595, 476927, 9988872, 239256001, 6449923155, 193258438649, 6371078552262, 229165569442783, 8931086129716275, 374876451878640767, 16860509248409118240, 808929567471759034753, 41238547431811301654163

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

Column k=3 of A305466.

Cf. A305459, A305472.

Programs

PARI

{a(n) = sum(k=0, n/2, ((n-k)!/k!)*binomial(n-k, k)*3^(n-2*k)*(-1)^k)}

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