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A348312
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a(n) = n! * Sum_{k=0..n-1} 3^k / k!.
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1
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0, 1, 8, 51, 312, 1965, 13248, 97839, 800208, 7260921, 72806040, 801515979, 9620317512, 125071036389, 1751016829968, 26265324194055, 420245416687392, 7144172815479921, 128595113003161512, 2443307154421058019, 48866143111666389720, 1026189005418216656541, 22576158119430894214368
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..22.
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FORMULA
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E.g.f.: x * exp(3*x) / (1 - x).
a(0) = 0; a(n) = n * (a(n-1) + 3^(n-1)).
a(n) ~ exp(3)*n!. - Stefano Spezia, Oct 11 2021
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MATHEMATICA
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Table[n! Sum[3^k/k!, {k, 0, n - 1}], {n, 0, 22}]
nmax = 22; CoefficientList[Series[x Exp[3 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, 3^k/k!); \\ Michel Marcus, Oct 11 2021
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CROSSREFS
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Cf. A007526, A053486, A066534, A348314.
Sequence in context: A055147 A014829 A048438 * A295602 A226199 A267637
Adjacent sequences: A348309 A348310 A348311 * A348313 A348314 A348315
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Oct 11 2021
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STATUS
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approved
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