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A365269
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a(n) = Product_{k=1..n} A002720(k).
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1
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1, 2, 14, 476, 99484, 153802264, 2049722772328, 268353804798726416, 386893462638663037013264, 6798536031341327693983294520096, 1595359632648441879172205168815801694176, 5432770180592069558569584672506997142250856260032
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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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log(a(n)) ~ log(BarnesG(n+2)) + 4*n^(3/2)/3 - n*log(n)/4 - (1/4 + log(2) + log(Pi)/2)*n + 55*sqrt(n)/24.
log(a(n)) ~ n^2*log(n)/2 - 3*n^2/4 + 4*n^(3/2)/3 + 3*n*log(n)/4 - (5/4 + log(2)/2)*n + 55*sqrt(n)/24.
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MATHEMATICA
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Table[Product[k! * LaguerreL[k, -1], {k, 1, n}], {n, 0, 15}]
Table[BarnesG[n+2] * Product[LaguerreL[k, -1], {k, 1, n}], {n, 0, 15}]
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PROG
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(Python)
from math import prod, factorial, comb
def A365269(n): return prod(sum(factorial(m)*comb(k, m)**2 for m in range(k+1)) for k in range(1, n+1)) # Chai Wah Wu, Aug 31 2023
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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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