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

0,3

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

Formula

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))]

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 *)

Crossrefs

Cf. A000898, A121966.

Sequence in context: A153968 A153965 A121221 * A279069 A257609 A087783

Adjacent sequences: A122595 A122596 A122597 * A122599 A122600 A122601

Keyword

sign

Author

Roger L. Bagula, Sep 19 2006

Extensions

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

Status

approved