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

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

Offset: 4

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

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]

Programs

Magma

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

Mathematica

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

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)

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