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A305472
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a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) - 2*a(n-2).
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2
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1, 3, 16, 138, 1624, 24084, 430264, 8987376, 214836496, 5782610640, 173048646208, 5699040103584, 204819346436608, 7976556430820544, 334605731401589632, 15041304800209892352, 721313418947271653632, 36756901756710434550528
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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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PROG
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(PARI) {a(n) = sum(k=0, n/2, ((n-k)!/k!)*binomial(n-k, k)*3^(n-2*k)*(-2)^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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