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A305472 a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) - 2*a(n-2). 2
1, 3, 16, 138, 1624, 24084, 430264, 8987376, 214836496, 5782610640, 173048646208, 5699040103584, 204819346436608, 7976556430820544, 334605731401589632, 15041304800209892352, 721313418947271653632, 36756901756710434550528 (list; graph; refs; listen; history; text; internal format)
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) ~ BesselJ(0, 2*sqrt(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)*(-2)^k)}

CROSSREFS

Cf. A305460, A305471.

Sequence in context: A230320 A230318 A006057 * A002719 A020554 A062874

Adjacent sequences:  A305469 A305470 A305471 * A305473 A305474 A305475

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jun 02 2018

STATUS

approved

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Last modified May 6 19:52 EDT 2021. Contains 343586 sequences. (Running on oeis4.)