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

%I A305471 #16 Jun 03 2018 03:44:43
%S A305471 1,3,17,150,1783,26595,476927,9988872,239256001,6449923155,
%T A305471 193258438649,6371078552262,229165569442783,8931086129716275,
%U A305471 374876451878640767,16860509248409118240,808929567471759034753,41238547431811301654163
%N A305471 a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) - a(n-2).
%C A305471 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 A305471 Seiichi Manyama, <a href="/A305471/b305471.txt">Table of n, a(n) for n = 0..380</a>
%F A305471 a(n) = Sum_{k=0..floor(n/2)} ((n-k)!/k!)*binomial(n-k,k)*3^(n-2*k)*(-1)^k.
%F A305471 a(n) ~ BesselJ(0, 2/3) * n! * 3^n. - _Vaclav Kotesovec_, Jun 03 2018
%o A305471 (PARI) {a(n) = sum(k=0, n/2, ((n-k)!/k!)*binomial(n-k, k)*3^(n-2*k)*(-1)^k)}
%Y A305471 Column k=3 of A305466.
%Y A305471 Cf. A305459, A305472.
%K A305471 nonn
%O A305471 0,2
%A A305471 _Seiichi Manyama_, Jun 02 2018