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A054777
a(n) = 4*n*(4*n-1)*(4*n-2)*(4*n-3).
1
0, 24, 1680, 11880, 43680, 116280, 255024, 491400, 863040, 1413720, 2193360, 3258024, 4669920, 6497400, 8814960, 11703240, 15249024, 19545240, 24690960, 30791400, 37957920, 46308024, 55965360, 67059720, 79727040, 94109400, 110355024, 128618280, 149059680, 171845880
OFFSET
0,2
REFERENCES
L. B. W. Jolley, Summation of Series, Dover, 1961.
Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 268.
LINKS
Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")
FORMULA
a(n) = A052762(4n) = 24*A060541(n).
Sum_{n>=1} 1/a(n) = log(2)/4 - Pi/24 = 0.0423871012404116... [Jolley eq. 242] - Benoit Cloitre, Apr 05 2002
G.f. -24*x*(1 + 65*x + 155*x^2 + 35*x^3) / (x-1)^5. - R. J. Mathar, Oct 03 2011
Sum_{n>=1} (-1)^(n+1)/a(n) = log(sqrt(2)-1)/(6*sqrt(2)) - log(2)/24 + (1/(6*sqrt(2)) - 1/16)*Pi. - Amiram Eldar, Mar 08 2022
MATHEMATICA
a[n_] := 4*n*(4*n-1)*(4*n-2)*(4*n-3); Array[a, 40, 0] (* Amiram Eldar, Mar 08 2022 *)
PROG
(Magma) [4*n*(4*n-1)*(4*n-2)*(4*n-3): n in [0..30]]; // Vincenzo Librandi, Oct 04 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Henry Bottomley, May 19 2000
STATUS
approved