A054777 a(n) = 4*n*(4*n-1)*(4*n-2)*(4*n-3).

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, Blackie & Son Limited, London and Glasgow, 1954. See exercise 107 at page 268.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = A052762(4*n) = 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

From Elmo R. Oliveira, Sep 07 2025: (Start)

E.g.f.: 8*x*(3 + 102*x + 144*x^2 + 32*x^3)*exp(x).

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). (End)

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

Cf. A052762, A060541, A104188.

Sequence in context: A112389 A187634 A229430 * A301392 A084224 A348589

Adjacent sequences: A054774 A054775 A054776 * A054778 A054779 A054780

Keyword

easy,nonn

Author

Henry Bottomley, May 19 2000

Status

approved