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 A123022 a(n)=n!*b(n) where b(0)=b(1)=1, b(n)=(n-4)b(n-2)/[n(n-1)] for n>=2. 0
 1, 1, -2, -1, 0, -1, 0, -3, 0, -15, 0, -105, 0, -945, 0, -10395, 0, -135135, 0, -2027025, 0, -34459425, 0, -654729075, 0, -13749310575, 0, -316234143225, 0, -7905853580625, 0, -213458046676875, 0, -6190283353629375, 0, -191898783962510625, 0, -6332659870762850625, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES Richard Bronson, Schaum's Outline of Modern Introductory Differential Equations, MacGraw-Hill, New York,1973, page 99, solved problem 19.1. LINKS FORMULA G.f.: (1 - G(0))*x^4/(1+x) +1 +x -2*x^2 -x^3, where G(k)= 1 + x*(2*k+1)/(1 - x/(x + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 07 2013 MAPLE b[0]:=1: b[1]:=1: for n from 2 to 40 do b[n]:=(n-4)*b[n-2]/n/(n-1) od: seq(n!*b[n], n=0..40); MATHEMATICA a[n_] := a[n] = (n - 4)*a[n - 2]/(n*(n - 1)); a[0] = 1; a[1] = 1; Table[a[n]*n!, {n, 0, 30}] CROSSREFS Sequence in context: A265674 A229297 A116675 * A072943 A072175 A280712 Adjacent sequences:  A123019 A123020 A123021 * A123023 A123024 A123025 KEYWORD sign AUTHOR Roger L. Bagula, Sep 24 2006 EXTENSIONS Edited by N. J. A. Sloane, Oct 01 2006 and Nov 24 2006 STATUS approved

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Last modified April 21 17:36 EDT 2021. Contains 343156 sequences. (Running on oeis4.)