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

%I

%S 1,3,16,138,1624,24084,430264,8987376,214836496,5782610640,

%T 173048646208,5699040103584,204819346436608,7976556430820544,

%U 334605731401589632,15041304800209892352,721313418947271653632,36756901756710434550528

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

%C 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.

%H Seiichi Manyama, <a href="/A305472/b305472.txt">Table of n, a(n) for n = 0..380</a>

%F a(n) ~ BesselJ(0, 2*sqrt(2)/3) * n! * 3^n. - _Vaclav Kotesovec_, Jun 03 2018

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

%Y Cf. A305460, A305471.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jun 02 2018

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Last modified June 22 17:18 EDT 2021. Contains 345388 sequences. (Running on oeis4.)