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 A358446 a(n) = n! * Sum_{k=0..floor(n/2)} 1/binomial(n-k, k). 3
 1, 1, 4, 9, 56, 190, 1704, 7644, 93120, 516240, 8136000, 53523360, 1047548160, 7961241600, 187132377600, 1611967392000, 44311886438400, 426483893606400, 13428757601280000, 142790947407360000, 5066854992138240000, 58981696577556480000, 2328441680297779200000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..449 FORMULA 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. a(n) ~ n! * (3 + (-1)^n)/2. - Vaclav Kotesovec, Nov 17 2022 a(n) = Sum_{k=0..floor(n/2)} A143216(n, k)/A344391(n, k). - Peter Luschny, Nov 17 2022 MAPLE 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 PROG (Maxima) a(n):=factorial(n)*sum(1/binomial(n-k, k), k, 0, floor(n/2)); (SageMath) def A358446(n): return sum(A143216(n, k) // A344391(n, k) for k in range((n+2)//2)) print([A358446(n) for n in range(23)]) # Peter Luschny, Nov 17 2022 CROSSREFS Cf. A003149, A143216, A344391. Sequence in context: A219894 A203464 A360514 * A152284 A109717 A197859 Adjacent sequences: A358443 A358444 A358445 * A358447 A358448 A358449 KEYWORD nonn AUTHOR Vladimir Kruchinin, Nov 16 2022 STATUS approved

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Last modified June 5 07:09 EDT 2023. Contains 363130 sequences. (Running on oeis4.)