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A022224 Gaussian binomial coefficients [ n,6 ] for q = 6. 1
1, 55987, 2686760143, 125936508182839, 5880230843762528935, 274383335413146060060487, 12801903280371155724242141959, 597287733061433620469903134280071, 27867073064694433516284053323814269063 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,2

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 = 6..200

FORMULA

G.f.: x^6/((1-x)*(1-6*x)*(1-36*x)*(1-216*x)*(1-1296*x)*(1-7776*x)*(1-46656*x)). - Vincenzo Librandi, Aug 12 2016

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

MATHEMATICA

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

PROG

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

(Magma) r:=6; 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=6; 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: A254515 A254815 A229436 * A230336 A252320 A252020

Adjacent sequences: A022221 A022222 A022223 * A022225 A022226 A022227

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 December 3 15:12 EST 2022. Contains 358534 sequences. (Running on oeis4.)