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A332695
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a(n) = (-1)^n * n! * Laguerre(n, 6*n).
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5
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1, 5, 98, 3234, 149784, 8927880, 650696400, 56061791856, 5574017768832, 628158472212096, 79123082415148800, 11015976349601752320, 1679832851707998600192, 278440504042352431942656, 49846084962712218734045184, 9584526091509128369970432000, 1970059291620925696814892810240
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OFFSET
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0,2
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COMMENTS
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For m > 4, (-1)^n * n! * Laguerre(n, m*n) ~ sqrt(1/2 + (m-2)/(2*sqrt(m*(m-4)))) * exp((m - 2 - sqrt(m*(m-4)))*n/2) * ((m - 2 + sqrt(m*(m-4)))/2)^n * n^n.
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LINKS
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FORMULA
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a(n) ~ sqrt(1/2 + 1/sqrt(3)) * 2^n * exp((2-sqrt(3))*n) * ((1 + sqrt(3))/2)^(2*n) * n^n.
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MATHEMATICA
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Table[(-1)^n * n! * LaguerreL[n, 6*n], {n, 0, 20}]
Flatten[{1, Table[n!*Sum[Binomial[n, k] * (-1)^(n-k) * 6^k * n^k / k!, {k, 0, n}], {n, 1, 20}]}]
Table[(-1)^n * n! * Hypergeometric1F1[-n, 1, 6*n], {n, 0, 20}]
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PROG
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(PARI) a(n) = (-1)^n*n!*pollaguerre(n, 0, 6*n); \\ Michel Marcus, Feb 05 2021
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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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