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A102094 a(n) = (2*n-1)*(2*n+1)^2. 0
9, 75, 245, 567, 1089, 1859, 2925, 4335, 6137, 8379, 11109, 14375, 18225, 22707, 27869, 33759, 40425, 47915, 56277, 65559, 75809, 87075, 99405, 112847, 127449, 143259, 160325, 178695, 198417, 219539, 242109, 266175, 291785, 318987, 347829, 378359, 410625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sum_{n=1..infinity} 1/a(n) = (12 - Pi^2)/16 Sum_{n=1..infinity} n/a(n) = (4 - Pi^2)/32

REFERENCES

G. Boros and V. Moll, Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, Cambridge University Press, Cambridge, 2004, p. 123.

J. Ewell, An Eulerian Method for Representing Pi^2 by Series, The Rocky Mountain Journal of Mathematics 1992 v.22, pp. 165-168.

LINKS

Table of n, a(n) for n=1..37.

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

FORMULA

a(1)=9, a(2)=75, a(3)=245, a(4)=567, a(n)=4*a(n-1)-6*a(n-2)+ 4*a(n-3)- a(n-4) -- From Harvey P. Dale, Jul 24 2012

G.f.: (x^3-x^2+39*x+9)/(x-1)^4 -- From Harvey P. Dale, Jul 24 2012

MATHEMATICA

Table[(2n-1)(2n+1)^2, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {9, 75, 245, 567}, 40] (* Harvey P. Dale, Jul 24 2012 *)

CROSSREFS

Cf. A002388.

Sequence in context: A231910 A028991 A249396 * A274311 A281804 A210045

Adjacent sequences:  A102091 A102092 A102093 * A102095 A102096 A102097

KEYWORD

easy,nonn

AUTHOR

Gerald McGarvey, Feb 13 2005

EXTENSIONS

More terms from Harvey P. Dale, Jul 24 2012

STATUS

approved

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Last modified October 17 16:34 EDT 2018. Contains 316285 sequences. (Running on oeis4.)