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A358446
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a(n) = n! * Sum_{k=0..floor(n/2)} 1/binomial(n-k, k).
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3
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1, 1, 4, 9, 56, 190, 1704, 7644, 93120, 516240, 8136000, 53523360, 1047548160, 7961241600, 187132377600, 1611967392000, 44311886438400, 426483893606400, 13428757601280000, 142790947407360000, 5066854992138240000, 58981696577556480000, 2328441680297779200000
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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.: (2*x+1)/((x-1)*(x+1)*(x^2-x-1))-(x*log((1-x)^2*(x+1)))/(-x^2+x+1)^2.
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MAPLE
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egf := (2*x+1)/((x-1)*(x+1)*(x^2-x-1))-(x*log((1-x)^2*(x+1)))/(-x^2+x+1)^2:
ser := series(egf, x, 22): seq(n!*coeff(ser, x, n), n = 0..20); # Peter Luschny, Nov 17 2022
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PROG
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(Maxima)
a(n):=factorial(n)*sum(1/binomial(n-k, k), k, 0, floor(n/2));
(SageMath)
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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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