A123025 a(n) = n!*b(n), where b(n) = (1 + n - n^2)*b(n-2)/(n*(n-1)), b(0) = b(1) = 1.

1, 1, -1, -5, 11, 95, -319, -3895, 17545, 276545, -1561505, -30143405, 204557155, 4672227775, -37024845055, -976495604975, 8848937968145, 264630308948225, -2698926080284225, -90238935351344725, 1022892984427721275, 37810113912213439775, -471553665821179507775

Offset

0,4

References

Richard Bronson, Schaum's Outline of Modern Introductory Differential Equations, MacGraw-Hill, New York,1973, page 107, solved problem 19.17

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

Formula

a(n) = n!*b(n), where b(n) = (1 + n - n^2)*b(n-2)/(n*(n-1)) and b(0) = b(1) = 1.

a(n) = (1 + n - n^2)*a(n-2), with a(0) = a(1) = 1. - G. C. Greubel, Jul 20 2021

Mathematica

b[n_]:= b[n]= If[n<2, 1, (1 +n -n^2)*b[n-2]/(n*(n-1))]; Table[b[n]*n!, {n, 0, 30}]

Prog

(Magma)
function a(n)
  if n lt 2 then return 1;
  else return (1 +n -n^2)*a(n-2);
  end if; return a;
end function;
[a(n): n in [0..30]]; // G. C. Greubel, Jul 20 2021
(Sage)
def b(n): return 1 if (n<2) else (1 +n -n^2)*b(n-2)/(n*(n-1))
def a(n): return factorial(n)*b(n)
[a(n) for n in (0..30)] # G. C. Greubel, Jul 20 2021

Crossrefs

Cf. A123026.

Sequence in context: A042761 A372126 A224270 * A053778 A030079 A066596

Adjacent sequences: A123022 A123023 A123024 * A123026 A123027 A123028

Keyword

sign

Author

Roger L. Bagula, Sep 24 2006

Extensions

Edited by N. J. A. Sloane, Jan 06 2009

Edited by G. C. Greubel, Jul 20 2021

Status

approved