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A171220 a(n) = (2n + 1)*5^n. 1
1, 15, 125, 875, 5625, 34375, 203125, 1171875, 6640625, 37109375, 205078125, 1123046875, 6103515625, 32958984375, 177001953125, 946044921875, 5035400390625, 26702880859375, 141143798828125, 743865966796875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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).

LINKS

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)

FORMULA

a(n) = 10*a(n-1) - 25*a(n-2).

O.g.f: (1+5*x)/(1-5*x)^2.

PROG

(PARI) a(n)=(2*n+1)*5^n

(MAGMA) [(2*n+1)*5^n: n in [0..25]]; // Vincenzo Librandi, Jun 08 2011

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

Jaume Oliver Lafont, Dec 05 2009

STATUS

approved

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Last modified July 21 17:20 EDT 2019. Contains 325198 sequences. (Running on oeis4.)