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A022223 Gaussian binomial coefficients [ n,5 ] for q = 6. 1
1, 9331, 74630671, 583026951031, 4537117983992551, 35285166561510069127, 274383335413146060060487, 2133612436978999661759040967, 16590980186519640252690843276487, 129011474730413928552335877184470727 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

REFERENCES

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 5..200

FORMULA

G.f.: x^5/((1-x)*(1-6*x)*(1-36*x)*(1-216*x)*(1-1296*x)*(1-7776*x)). - Vincenzo Librandi, Aug 12 2016

a(n) = Product_{i=1..5} (6^(n-i+1)-1)/(6^i-1), by definition. - Vincenzo Librandi, Aug 12 2016

MATHEMATICA

Table[QBinomial[n, 5, 6], {n, 5, 20}] (* Vincenzo Librandi, Aug 12 2016 *)

PROG

(Sage) [gaussian_binomial(n, 5, 6) for n in xrange(5, 15)] # Zerinvary Lajos, May 27 2009

(MAGMA) r:=5; q:=6; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 12 2016

(PARI) r=5; q=6; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 07 2018

CROSSREFS

Sequence in context: A048132 A241935 A229435 * A172914 A209792 A004934

Adjacent sequences:  A022220 A022221 A022222 * A022224 A022225 A022226

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Offset changed by Vincenzo Librandi, Aug 12 2016

STATUS

approved

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Last modified March 26 05:43 EDT 2019. Contains 321481 sequences. (Running on oeis4.)