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A052675
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Expansion of e.g.f. (1-x)/(1-5*x).
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1
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1, 4, 40, 600, 12000, 300000, 9000000, 315000000, 12600000000, 567000000000, 28350000000000, 1559250000000000, 93555000000000000, 6081075000000000000, 425675250000000000000, 31925643750000000000000
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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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E.g.f.: (1 - x)/(1 - 5*x).
D-finite Recurrence: a(0)=1, a(1)=4, a(n) = 5*n*a(n-1).
a(n) = 4*5^(n-1)*n!, n>0.
G.f.: (4/5)*(Hypergeometric2F0([1, 1], [], 5*x) + 1/4). - G. C. Greubel, Jun 12 2022
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MAPLE
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spec := [S, {S=Sequence(Prod(Sequence(Z), Union(Z, Z, Z, Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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Table[(4/5)*(5^n*n! + Boole[n==0]/4), {n, 0, 50}] (* G. C. Greubel, Jun 12 2022 *)
With[{nn=20}, CoefficientList[Series[(1-x)/(1-5x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 31 2023 *)
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PROG
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(SageMath) [4*factorial(n)*5^(n-1) + bool(n==0)/5 for n in (0..40)] # G. C. Greubel, Jun 12 2022
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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