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A091045
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Partial sums of powers of 17 (A001026).
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41
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1, 18, 307, 5220, 88741, 1508598, 25646167, 435984840, 7411742281, 125999618778, 2141993519227, 36413889826860, 619036127056621, 10523614159962558, 178901440719363487, 3041324492229179280, 51702516367896047761
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OFFSET
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1,2
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COMMENTS
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17^a(n) is largest power of 17 dividing (17^n)!.
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=17, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n)=det(A). - Milan Janjic, Feb 21 2010
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n-1} 17^k = (17^n - 1)/16.
G.f.: x/((1 - 17*x)*(1 - x))= (1/(1 - 17*x) - 1/(1 - x))/16.
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MAPLE
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ListTools:-PartialSums([seq(17^k, k=0..30)]); # Robert Israel, Feb 18 2018
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MATHEMATICA
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PROG
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(Sage) [gaussian_binomial(n, 1, 17) for n in range(1, 18)] # Zerinvary Lajos, May 28 2009
(Maxima) makelist(sum(17^k, k, 0, n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
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CROSSREFS
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Cf. similar sequences of the form (k^n-1)/(k-1) with k prime: A000225 (k=2), A003462 (k=3), A003463 (k=5), A023000 (k=7), A016123 (k=11), A091030 (k=13), this sequence (k=17), A218722 (k=19), A218726 (k=23), A218732 (k=29), A218734 (k=31), A218740 (k=37), A218744 (k=41), A218746 (k=43), A218750 (k=47).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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