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A320433
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Expansion of e.g.f. exp(4 * (1 - exp(x)) + x).
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1
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1, -3, 5, 5, -43, -27, 597, 805, -11883, -40475, 265685, 2133157, -3405803, -107760283, -301542315, 4458255397, 42421260949, -45046794011, -3365690666283, -19844416105563, 138274174035221, 2917746747446373, 11092963732101461, -207438902364296411, -3205301465165742187
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..24.
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FORMULA
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a(0) = 1 and a(n) = a(n-1) - 4 * Sum_{k=0..n-1} binomial(n-1,k) * a(k) for n > 0.
a(n) = exp(4) * Sum_{k>=0} (k + 1)^n * (-4)^k / k!.
a(n) = Sum_{k=0..n} binomial(n,k) * Bell(k, -4). - Vaclav Kotesovec, Jul 06 2020
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MATHEMATICA
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m = 24; Range[0, m]! * CoefficientList[Series[Exp[4 * (1 - Exp[x]) + x], {x, 0, m}], x] (* Amiram Eldar, Jul 06 2020 *)
Table[Sum[Binomial[n, k] * BellB[k, -4], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Jul 06 2020 *)
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PROG
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(PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(4*(1-exp(x))+x)))
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CROSSREFS
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Column k=4 of A335977.
Cf. A078945, A335982.
Sequence in context: A072624 A147976 A019247 * A165142 A231809 A186969
Adjacent sequences: A320430 A320431 A320432 * A320434 A320435 A320436
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KEYWORD
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sign
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AUTHOR
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Seiichi Manyama, Jul 06 2020
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STATUS
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approved
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