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A022209 Gaussian binomial coefficients [ n,10 ] for q = 4. 1
1, 1398101, 1563749404581, 1665737215212030181, 1753501675591663698472421, 1840477112202685809580351554021, 1930351405154232225472089767795511781, 2024243704924003025844684284218991557841381 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,2

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 = 10..170

FORMULA

G.f.: x^10/((1-x)*(1-4*x)*(1-16*x)*(1-64*x)*(1-256*x)*(1-1024*x)*(1-4096*x)*(1-16384*x)*(1-65536*x)*(1-262144*x)*(1-1048576*x)). - Vincenzo Librandi, Aug 11 2016

a(n) = Product_{i=1..10} (4^(n-i+1)-1)/(4^i-1), by definition. - Vincenzo Librandi, Aug 11 2016

MATHEMATICA

Table[QBinomial[n, 10, 4], {n, 10, 20}] (* Vincenzo Librandi, Aug 11 2016 *)

PROG

(Sage) [gaussian_binomial(n, 10, 4) for n in xrange(10, 18)] # Zerinvary Lajos, May 25 2009

(MAGMA) r:=10; q:=4; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 11 2016

(PARI) r=10; q=4; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 04 2018

CROSSREFS

Sequence in context: A052242 A234548 A069315 * A203883 A064871 A237397

Adjacent sequences:  A022206 A022207 A022208 * A022210 A022211 A022212

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Offset changed by Vincenzo Librandi, Aug 11 2016

STATUS

approved

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Last modified March 24 06:56 EDT 2019. Contains 321444 sequences. (Running on oeis4.)