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A069777
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Triangle of q-factorial numbers n!_q, for (n,q) = (0,0), (1,0), (0,1), (2,0), etc.
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5
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1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 6, 3, 1, 1, 1, 24, 21, 4, 1, 1, 1, 120, 315, 52, 5, 1, 1, 1, 720, 9765, 2080, 105, 6, 1, 1, 1, 5040, 615195, 251680, 8925, 186, 7, 1, 1, 1, 40320, 78129765, 91611520, 3043425, 29016, 301, 8, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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REFERENCES
| Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
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FORMULA
| T(n,q) = prod(k=1..n, (q^k - 1) / (q - 1) )
T(n,k) = prod(n1=k..n-1, A104878(n1,k) ) [Johannes W. Meijer, Aug 21 2011]
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MAPLE
| From Johannes W. Meijer, Aug 21 2011: (Start)
A069777 := proc(n, k) local n1: mul(A104878(n1, k), n1=k..n-1) end: A104878 := proc(n, k): if k = 0 then 1 elif k=1 then n elif k>=2 then (k^(n-k+1)-1)/(k-1) fi: end: seq(seq(A069777(n, k), k=0..n), n=0..9);
nmax:=9: T(0, 0):=1: for n from 1 to nmax do T(n, 0):=1: T(n, 1):= (n-1)! od: for q from 2 to nmax do for n from 0 to nmax do T(n+q, q) := product((q^k - 1)/(q - 1), k= 1..n) od: od: for n from 0 to nmax do seq(T(n, k), k=0..n) od; seq(seq(T(n, k), k=0..n), n=0..nmax); # (End)
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CROSSREFS
| Cf. A000142, A005329, A015001, A015002, A069778, A069779.
Sequence in context: A129110 A112624 A139329 * A064992 A089759 A088152
Adjacent sequences: A069774 A069775 A069776 * A069778 A069779 A069780
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 07 2002
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