A022248 Gaussian binomial coefficients [ n,8 ] for q = 8.

1, 19173961, 326791806956681, 5493386001237942388361, 92186229916592298695053497993, 1546675492323688689677277254864590473, 25949007804224083420097621839124559742097033

Offset

8,2

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 = 8..140

Formula

a(n) = Product_{i=1..8} (8^(n-i+1)-1)/(8^i-1), by definition. - Vincenzo Librandi, Aug 06 2016

G.f.: x^8/((1 - x)*(1 - 8*x)*(1 - 64*x)*(1 - 512*x)*(1 - 4096*x)*(1 - 32768*x)*(1 - 262144*x)*(1 - 2097152*x)*(1 - 16777216*x)). - Ilya Gutkovskiy, Aug 06 2016

Mathematica

Table[QBinomial[n, 8, 8], {n, 8, 20}] (* Vincenzo Librandi, Aug 06 2016 *)

Prog

(Sage) [gaussian_binomial(n, 8, 8) for n in range(8, 15)] # Zerinvary Lajos, May 25 2009
(Magma) r:=8; q:=8; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 06 2016

Crossrefs

Sequence in context: A138025 A184790 A183697 * A224627 A038683 A017287

Adjacent sequences: A022245 A022246 A022247 * A022249 A022250 A022251

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

Offset changed by Vincenzo Librandi, Aug 06 2016

Status

approved