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A305471
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a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) - a(n-2).
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3
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1, 3, 17, 150, 1783, 26595, 476927, 9988872, 239256001, 6449923155, 193258438649, 6371078552262, 229165569442783, 8931086129716275, 374876451878640767, 16860509248409118240, 808929567471759034753, 41238547431811301654163
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..floor(n/2)} ((n-k)!/k!)*binomial(n-k,k)*3^(n-2*k)*(-1)^k.
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PROG
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(PARI) {a(n) = sum(k=0, n/2, ((n-k)!/k!)*binomial(n-k, k)*3^(n-2*k)*(-1)^k)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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