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A022217 Gaussian binomial coefficients [ n,10 ] for q = 5. 1
1, 12207031, 124176340230306, 1222439084242108174806, 11957012900737114492991256681, 116805081731088587940522831693775431, 1140747634121270227670449517400445860666056, 11140256209730412546658078532854767895273286916056 (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..150

FORMULA

G.f.: x^10/((1-x)*(1-5*x)*(1-25*x)*(1-125*x)*(1-625*x)*(1-3125*x)*(1-15625*x)*(1-78125*x)*(1-390625*x)*(1-1953125*x)*(1-9765625*x)). - Vincenzo Librandi, Aug 10 2016

a(n) = Product_{i=1..10} (5^(n-i+1)-1)/(5^i-1), by definition. - Vincenzo Librandi, Aug 06 2016

MATHEMATICA

Table[QBinomial[n, 10, 5], {n, 10, 20}] (* Vincenzo Librandi, Aug 10 2016 *)

PROG

(Sage) [gaussian_binomial(n, 10, 5) for n in xrange(10, 17)] # Zerinvary Lajos, May 27 2009

(MAGMA)  r:=10; q:=5; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 10 2016

(PARI) r=10; q=5; 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: A204888 A268418 A286301 * A133373 A321987 A288272

Adjacent sequences:  A022214 A022215 A022216 * A022218 A022219 A022220

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Offset changed by Vincenzo Librandi, Aug 10 2016

STATUS

approved

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Last modified March 20 21:49 EDT 2019. Contains 321352 sequences. (Running on oeis4.)