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A123025
a(n) = n!*b(n), where b(n) = (1 + n - n^2)*b(n-2)/(n*(n-1)), b(0) = b(1) = 1.
3
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
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
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