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A171220
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a(n) = (2n + 1)*5^n.
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1
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1, 15, 125, 875, 5625, 34375, 203125, 1171875, 6640625, 37109375, 205078125, 1123046875, 6103515625, 32958984375, 177001953125, 946044921875, 5035400390625, 26702880859375, 141143798828125, 743865966796875
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OFFSET
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0,2
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COMMENTS
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Inserting x=1/sqrt(b) into the power series expansion of arctanh(x) yields the general BBP-type formula log((sqrt(b)+1)/(sqrt(b)-1))*sqrt(b)/2 = Sum_{k>=0} 1/((2k+1)b^k).
This sequence illustrates case b=5, with
Sum_{k>=0} 1/a(k) = sqrt(5)*log((1+sqrt(5))/2).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
David H. Bailey, Compendium of BBP formulas for mathematical constants (formula 53)
Index entries for linear recurrences with constant coefficients, signature (10,-25)
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FORMULA
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a(n) = 10*a(n-1) - 25*a(n-2).
O.g.f: (1+5*x)/(1-5*x)^2.
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PROG
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(PARI) a(n)=(2*n+1)*5^n
(MAGMA) [(2*n+1)*5^n: n in [0..25]]; // Vincenzo Librandi, Jun 08 2011
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CROSSREFS
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Cf. (2n+1)2^n A014480, (2n+1)*3^n A124647, (2n+1)*4^n A058962, (2n+1)9^n A155988, (2n+1)16^n A165283, (2n+1)25^n A166725.
Sequence in context: A264046 A027839 A034271 * A071080 A193365 A069975
Adjacent sequences: A171217 A171218 A171219 * A171221 A171222 A171223
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KEYWORD
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nonn,easy
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AUTHOR
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Jaume Oliver Lafont, Dec 05 2009
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STATUS
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approved
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