A122598 a(0) = 0; a(1) = 1; if n is odd then a(n) = 2*a(n-1) - (n-1)*a(n-2) otherwise a(n) = 2*(a(n-1) - (n-2)*a(n-2)).

0, 1, 2, 2, -4, -16, 0, 96, 192, -384, -3840, -3840, 69120, 184320, -1290240, -5160960, 25804800, 134184960, -557383680, -3530096640, 13005619200, 96613171200, -326998425600, -2779486617600, 8828957491200, 84365593804800, -255058771968000, -2703622982860800, 7855810176614400

Offset: 0

Author

Roger L. Bagula, Sep 19 2006

Keywords

• sign
• easy

References

• E. S. R. Gopal, Specific Heats at Low Temperatures, Plenum Press, New York, 1966, pages 36-40.

Links

• Robert Israel, Table of n, a(n) for n = 0..804

Crossrefs

Cf. A000898, A121966.

Programs

Maple

f:= proc(n) option remember;
if n::odd then 2*procname(n-1) - (n-1)*procname(n-2)
else 2*procname(n-1) - 2*(n-2)*procname(n-2)
fi
end proc:
f(0):= 0: f(1):= 1:
map(f, [$0..100]); # Robert Israel, Mar 15 2017

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = If[Mod[n, 2] == 1, 2*a[n - 1] - ( n - 1)*a[n - 2], 2*(a[n - 1] - (n - 2)*a[n - 2])] b = Table[a[n], {n, 0, 30}]
nxt[{n_,a_,b_}]:={n+1,b,If[EvenQ[n],2*b-n*a,2(b-(n-1)a)]}; Transpose[ NestList[ nxt,{1,0,1},30]][[2]] (* Harvey P. Dale, Dec 15 2014 *)

Formula

a(n) = 2*a(n-1) - (n-1)*a(n-2) for n odd > 1; a(n) = 2*(a(n-1) - (n-2)*a(n-2)) for n even > 1.

Extensions

Edited by N. J. A. Sloane, Oct 01 2006