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1, 1, 5, 125, 15625, 9765625, 30517578125, 476837158203125, 37252902984619140625, 14551915228366851806640625, 28421709430404007434844970703125
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Sequence given by the Hankel transform (see A001906 for definition) of A078009 = {1, 1, 6, 41, 306, 2426, 20076, 171481, ...}; example : det([1, 1, 6, 41; 1, 6, 41, 306; 6, 41, 306, 2426; 41, 306, 2426, 20076]) = 5^6 = 15625.
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FORMULA
| a(n+1) is the determinant of n X n matrix M_(i, j) = binomial(5i, j).
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MAPLE
| seq(5^(binomial(2+n, n)), n=-2..8); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2007
a:=n->mul (5^j, j=1..n): seq(a(n), n=-1..9); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 03 2007
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MATHEMATICA
| f[n_]:=5^n; lst={}; Do[a=f[n]; Do[a*=f[m], {m, n-1, 1, -1}]; AppendTo[lst, a], {n, 0, 20}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 10 2010]
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PROG
| (PARI) a(n)=5^binomial(n, 2) \\ Charles R Greathouse IV, Jan 11 2012
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CROSSREFS
| Cf. A006125, A047656, A053763, A053764.
Sequence in context: A154022 A013710 A202628 * A194502 A201839 A156956
Adjacent sequences: A109342 A109343 A109344 * A109346 A109347 A109348
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KEYWORD
| nonn,easy
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 21 2005
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