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A129196 a(n) = denominator(3*(3+(-1)^n)/(n+1)^3). 5
1, 4, 9, 32, 125, 36, 343, 256, 243, 500, 1331, 288, 2197, 1372, 1125, 2048, 4913, 972, 6859, 4000, 3087, 5324, 12167, 2304, 15625, 8788, 6561, 10976, 24389, 4500, 29791, 16384, 11979, 19652, 42875, 7776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Numerator of 3*(3+(-1)^n)/(n+1)^3 is A129197.

(1/(2*Pi))*int(exp(i*(n+1)*t)((t-Pi)/i)^3,t,0,2*Pi)) = (A129202(n)*Pi^2-A129203(n))/A129196(n) with i=sqrt(-1).

LINKS

Table of n, a(n) for n=0..35.

FORMULA

a(n) = A129204(n+1)/(5/3+(4/3)*cos(2*Pi*(n+1)/3)).

a(n) = denominator((1/(2*Pi))*int(exp(i*(n+1)*t)((t-Pi)/i)^3,t,0,2*Pi)) with i=sqrt(-1).

a(n) = denominator((Pi^2*(n+1)^2-6)/(n+1)^3).

a(n) = ((n+1)^3/(gcd(n+1,2)*gcd(n+1,3))). - Paul Barry, Oct 09 2007

a(n) = numerator of coefficient of x^6 in the Maclaurin expansion of -exp(-(n+1)*x^2). - Francesco Daddi, Aug 04 2011

CROSSREFS

Sequence in context: A149120 A219151 A057819 * A119574 A006393 A320920

Adjacent sequences:  A129193 A129194 A129195 * A129197 A129198 A129199

KEYWORD

nonn,frac,easy

AUTHOR

Paul Barry, Apr 02 2007, Apr 03 2007

STATUS

approved

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Last modified October 23 22:42 EDT 2019. Contains 328378 sequences. (Running on oeis4.)