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Sum of the digits of the sum of n!!, with n>=0.
3

%I #4 Aug 24 2012 10:49:59

%S 1,2,4,7,6,3,15,12,18,9,15,24,24,33,24,33,24,33,24,51,42,51,33,51,69,

%T 51,60,69,60,87,60,60,87,105,87,87,105,87,87,105,114,105,96,141,123,

%U 123,159,150,159,150,141,141,132,168,159,150,177,159,159,168,195,186,195

%N Sum of the digits of the sum of n!!, with n>=0.

%e 0!!=1

%e 1!!=1 -> 1+1=2

%e 2!!=2 -> 2+2=4

%e 3!!=3 -> 4+3=7

%e 4!!=8 -> 7+8=15 -> 1+5=6

%e 5!!=15 -> 15+15=30 -> 3+0=3

%p P:=proc(n) local i,j,k,w,sf; sf:=1; for i from 0 by 1 to n do k:=i; w:=i-2; while w>0 do k:=k*w; w:=w-2; od; sf:=sf+k; w:=0; k:=sf; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; print(w); od; end: P(100);

%K easy,nonn,base

%O 0,2

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 14 2007