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A254927
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Coefficient of x^n in Product_{k=0..n} (1+k*x)^k.
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1
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1, 8, 238, 15715, 1822678, 327061056, 83839010860, 29063729300694, 13090011332041111, 7428850394493811712, 5185703819680371737432, 4366227375438927437584444, 4363140133466727238167744916, 5104897162398639619205564019232, 6912594322573705179830176812524216
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) ~ exp(n+3/8) * n^(2*n-1/2) / (sqrt(2*Pi) * 3^n).
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MATHEMATICA
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Table[Coefficient[Expand[Product[(1+k*x)^k, {k, 0, n}]], x^n], {n, 1, 20}] (* or *)
p=1; Table[p=Expand[p*(1+n*x)^n]; Coefficient[p, x^n], {n, 1, 20}] (* faster *)
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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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