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A114806
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Nonuple factorial, 9-factorial, n!9, n!!!!!!!!!.
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12
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1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 22, 36, 52, 70, 90, 112, 136, 162, 190, 440, 756, 1144, 1610, 2160, 2800, 3536, 4374, 5320, 12760, 22680, 35464, 51520, 71280, 95200, 123760, 157464, 196840, 484880, 884520, 1418560, 2112320, 2993760, 4093600
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OFFSET
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0,3
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LINKS
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FORMULA
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D-finite with recurrence: a(0) = 1, a(n) = n for 1 <= n <= 9, a(n) = n*a(n-9) for n >= 10.
a(9*m) = 9^m*m!.
a(9*m+k) = 9^m*(9*m+k)*Gamma(m+k/9)/Gamma(k/9) for 1 <= k <= 8. (End)
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EXAMPLE
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a(10) = 10 * a(10-9) = 10 * a(1) = 10 * 1 = 10.
a(20) = 20 * a(20-9) = 20 * a(11) = 20 * (11*a(11-9)) = 20 * 11 * a(2) = 20 * 11 * 2 = 440.
a(30) = 30 * a(30-9) = 30 * a(21) = 30 * (21*a(21-9)) = 30 * 21 * a(12) = 30 * 21 * (12*a(12-9)) = 30 * 21 * 12 * 3 = 22680.
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MAPLE
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f:= proc(n) option remember;
n*procname(n-9)
end proc:
f(0):= 1: for n from 1 to 8 do f(n):= n od:
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MATHEMATICA
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NFactorialM[n_, m_] := Block[{k = n, p = Max[1, n]}, While[k > m, k -= m; p *= k]; p]; Array[ NFactorialM[#, 9] &, 44, 0] (* Robert G. Wilson v, May 10 2011 *)
a[n_]:= a[n]= If[n<1, 1, n*a[n-9]]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Aug 21 2019 *)
Table[Times@@Range[n, 1, -9], {n, 0, 50}] (* Harvey P. Dale, Nov 13 2021 *)
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PROG
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(PARI) a(n)=if(n<1, 1, n*a(n-9));
(Magma) b:=func< n | n le 9 select n else n*Self(n-9) >;
(Sage)
def a(n):
if (n<1): return 1
else: return n*a(n-9)
(GAP)
a:= function(n)
if n<1 then return 1;
else return n*a(n-9);
fi;
end;
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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