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A092471
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a(n) = Sum_{i+j+k=n, 0<=i<=n, 0<=j<=n, 0<=k<=n} (n+i+j)!/((i+j)! * j! * k!).
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1
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1, 5, 43, 495, 7281, 133173, 2945755, 76769759, 2306295265, 78492222693, 2985018589323, 125449316558415, 5773653823774929, 288808141870191765, 15601413322486382523, 905170780889312826303, 56136189828704013001665
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ 2^(2*n + 1/2) * n^n / exp(n - 3/2).
Recurrence: n*(2*n - 5)*a(n) = (2*n - 5)*(2*n - 1)*(2*n + 3)*a(n-1) - (2*n - 3)*(24*n^2 - 72*n + 29)*a(n-2) + (2*n - 9)*(2*n - 5)*(2*n - 1)*a(n-3) + (n-3)*(2*n - 1)*a(n-4). (End)
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PROG
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(PARI) a(n)=sum(i=0, n, sum(j=0, n, sum(k=0, n, if(i+j+k-n, 0, (n+i+j)!/(i+j)!/j!/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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