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%I #25 Dec 12 2020 22:03:28
%S 1,1,2,6,24,30,18,63,72,81,90,99,216,117,126,135,144,153,162,171,180,
%T 189,396,414,216,225,234,243,252,261,270,279,576,594,612,315,324,333,
%U 342,351,360,369,756,774,792,810,414,423,432,441,450,459,936,954,972
%N Digital factorial: a(0) = 1, a(n) = n * (the sum of the digits of a(n-1)).
%H Colin Barker, <a href="/A110728/b110728.txt">Table of n, a(n) for n = 0..1000</a>
%e a(4) = 24, a(5) = 5*(2+4) = 30, a(6) = 6*3 = 18.
%p a:= proc(n) option remember; `if`(n=0, 1,
%p n*add(i, i=convert(a(n-1), base, 10)))
%p end:
%p seq(a(n), n=0..60); # _Alois P. Heinz_, Dec 12 2020
%t DigitSum[n_, 10] := Total[IntegerDigits[n, 10]]; A110728[0] := 1; A110728[n_] := A110728[n] = n*DigitSum[A110728[n - 1], 10]; Table[A110728[n], {n, 0, 50}] (* _G. C. Greubel_, Sep 06 2017 *)
%o (PARI) s=vector(1001, n, 1); for(n=2, #s, s[n]=(n-1)*sumdigits(s[n-1])); s \\ _Colin Barker_, Nov 20 2014
%Y Cf. A000142, A007953, A089718, A110729.
%K base,easy,nonn
%O 0,3
%A _Amarnath Murthy_, Aug 09 2005
%E a(22) and a(32) corrected, name clarified, and more terms added by _Colin Barker_, Nov 20 2014
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