A006113 Gaussian binomial coefficient [ n,4 ] for q = 5. (Formerly M5479)

1, 781, 508431, 320327931, 200525284806, 125368356709806, 78360229974772306, 48975769621072897306, 30609934249224268600431, 19131218685276848401412931, 11957012900737114492991256681, 7473133215765585192791624069181, 4670708278954101902438990598678556

Offset

4,2

References

J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.

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

M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

Links

Vincenzo Librandi, Table of n, a(n) for n = 4..200

M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy)

Formula

G.f.: x^4/((1-x)*(1-5*x)*(1-25*x)*(1-125*x)*(1-625*x)). - Vincenzo Librandi, Aug 07 2016

a(n) = Product_{i=1..4} (5^(n-i+1)-1)/(5^i-1), by definition. - Vincenzo Librandi, Aug 06 2016

Maple

qBinom := proc(n, m, q)
        mul( (1-q^(n-i))/(1-q^(i+1)), i=0..m-1) ;
end proc:
A006113 := proc(n)
        qBinom(n, 4, 5) ;
end proc:
seq(A006113(n), n=4..16) ; # R. J. Mathar, Sep 28 2011

Mathematica

Table[QBinomial[n, 4, 5], {n, 4, 20}] (* Vincenzo Librandi, Aug 07 2016 *)

Prog

(Sage) [gaussian_binomial(n, 4, 5) for n in range(4, 14)] # Zerinvary Lajos, May 27 2009
(Magma) r:=4; q:=5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 07 2016

Crossrefs

Sequence in context: A141390 A038477 A236888 * A212947 A158398 A003914

Adjacent sequences: A006110 A006111 A006112 * A006114 A006115 A006116

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved