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A168386 Arithmetic derivative of the double factorial of n. 2

%I

%S 0,0,1,1,12,8,112,71,1472,1269,17408,14904,270336,204147,4199424,

%T 4143285,87834624,72462870,1797783552,1411253955,40414740480,

%U 36183623805,937430876160,845972658090,26095323709440,24311657884500,707908274749440,869872809558375

%N Arithmetic derivative of the double factorial of n.

%H Alois P. Heinz, <a href="/A168386/b168386.txt">Table of n, a(n) for n = 0..800</a>

%F a(n) = A003415(A006882(n)). - _R. J. Mathar_, Nov 26 2009

%p A003415 := proc(n) local pfs ; if n <= 1 then 0 ; else pfs := ifactors(n)[2] ; n*add(op(2,p)/op(1,p),p=pfs) ; fi; end proc:

%p A168386 := proc(n) A003415(doublefactorial(n)) ; end proc:

%p seq(A168386(n),n=1..80) ; # _R. J. Mathar_, Nov 26 2009

%p # second Maple program:

%p d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):

%p a:= proc(n) option remember;

%p `if`(n<2, 0, a(n-2)*n+doublefactorial(n-2)*d(n))

%p end:

%p seq(a(n), n=0..40); # _Alois P. Heinz_, Jun 06 2015

%Y Cf. A003415, A068311.

%K easy,nonn

%O 0,5

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Nov 24 2009

%E Program replaced by a structured program - _R. J. Mathar_, Nov 26 2009

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Last modified September 5 00:37 EDT 2015. Contains 261339 sequences.