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A131955 a(n) = sum of digits of (n!! + a(n-1)).

%I A131955 #18 Mar 03 2025 14:42:39
%S A131955 1,3,6,5,2,5,2,17,17,23,14,23,23,23,23,23,41,41,41,41,41,50,41,59,68,
%T A131955 59,68,59,68,86,86,104,95,95,104,86,104,86,122,95,104,113,149,95,140,
%U A131955 95,131,122,149,140,140,113,185,149,185,149,176,194,176,185,194,194,203
%N A131955 a(n) = sum of digits of (n!! + a(n-1)).
%H A131955 Robert Israel, <a href="/A131955/b131955.txt">Table of n, a(n) for n = 1..10000</a>
%e A131955 a(4) = Sum_digits(6+4!!) = Sum_digits(6+8) = Sum_digits(14) = 5.
%p A131955 P:=proc(n) local a,i,k,w; a:=0; for i from 1 by 1 to n do w:=0; k:=a+2^((1+2*i-cos(i*Pi))/4)*Pi^((cos(i*Pi)-1)/4)*GAMMA(1+1/2*i); while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; a:=w; print(a); od; end: P(100);
%p A131955 # alternative:
%p A131955 A[1]:= 1:
%p A131955 for n from 2 to 100 do
%p A131955   A[n]:= convert(convert(doublefactorial(n)+A[n-1],base,10),`+`);
%p A131955 od:
%p A131955 seq(A[i],i=1..100); # _Robert Israel_, Oct 29 2020
%t A131955 s={1};Do[AppendTo[s,DigitSum[n!!+s[[-1]]]],{n,2,63}];s (* _James C. McMahon_, Mar 03 2025 *)
%Y A131955 Cf. A055263, A131954.
%K A131955 easy,nonn,base,look
%O A131955 1,2
%A A131955 _Paolo P. Lava_ and _Giorgio Balzarotti_, Jul 31 2007
%E A131955 Offset corrected by _Robert Israel_, Oct 29 2020