A006044 a(n) = 4^(n-4)*(n-1)*(n-2)*(n-3). (Formerly M4290)

6, 96, 960, 7680, 53760, 344064, 2064384, 11796480, 64880640, 346030080, 1799356416, 9160359936, 45801799680, 225485783040, 1095216660480, 5257039970304, 24970939858944, 117510305218560, 548381424353280, 2539871860162560, 11683410556747776, 53409876830846976

Offset

4,1

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 4..1000

Frank A. Haight, Overflow at a traffic light, Biometrika, 46 (1959), 420-424.

Frank A. Haight, Overflow at a traffic light, Biometrika, 46 (1959), 420-424. (Annotated scanned copy)

Frank A. Haight, Letter to N. J. A. Sloane, n.d..

Index entries for linear recurrences with constant coefficients, signature (16,-96,256,-256).

Formula

G.f. = 6*x^4/(1-4*x)^4. - Emeric Deutsch, Apr 29 2004

a(n) = 6*A038846(n). - R. J. Mathar , Mar 22 2013

E.g.f.: (3 + exp(4*x)*(32*x^3 - 24*x^2 + 12*x - 3))/128. - Stefano Spezia, Jan 01 2023

From Amiram Eldar, Jan 08 2023: (Start)

Sum_{n>=4} 1/a(n) = 18*log(4/3) - 5.

Sum_{n>=4} (-1)^n/a(n) = 50*log(5/4) - 11. (End)

Mathematica

a[n_] := 4^(n - 4)*(n - 1)*(n - 2)*(n - 3); Array[a, 25, 4] (* Amiram Eldar, Jan 08 2023 *)

Prog

(Magma) [4^(n-4)*(n-3)*(n-2)*(n-1): n in [4..30]]; // Vincenzo Librandi, Aug 14 2011

Crossrefs

Cf. A000142, A006043, A038846, A154120.

Column k=3 of square array A152818. - Paul Curtz, Dec 17 2008 [corrected by Omar E. Pol, Jan 07 2009]

Sequence in context: A055358 A030989 A288845 * A202078 A227262 A001805

Adjacent sequences: A006041 A006042 A006043 * A006045 A006046 A006047

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Apr 29 2004

Erroneous reference deleted by Martin J. Erickson (erickson(AT)truman.edu), Nov 03 2010

Entry revised by N. J. A. Sloane, Dec 27 2021

Status

approved