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A348314
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a(n) = n! * Sum_{k=0..n-1} 4^k / k!.
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1
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0, 1, 10, 78, 568, 4120, 30864, 244720, 2088832, 19389312, 196514560, 2173194496, 26128665600, 339890756608, 4759410116608, 71395178280960, 1142340032364544, 19419853564641280, 349557673401188352, 6641597100292636672, 132831947503410872320, 2789470920661372502016
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: x * exp(4*x) / (1 - x).
a(0) = 0; a(n) = n * (a(n-1) + 4^(n-1)).
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MATHEMATICA
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Table[n! Sum[4^k/k!, {k, 0, n - 1}], {n, 0, 21}]
nmax = 21; CoefficientList[Series[x Exp[4 x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
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PROG
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(PARI) a(n) = n!*sum(k=0, n-1, 4^k/k!); \\ Michel Marcus, Oct 11 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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