A022216 Gaussian binomial coefficients [ n,9 ] for q = 5.

1, 2441406, 4967053120931, 9779511680526143556, 19131218685276848401412931, 37377622327704219905090668384806, 73007841108236063781239140920167306681, 142595264882979563844964491038787206333791056

Offset

9,2

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 = 9..170

Formula

G.f.: x^9/((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)). - Vincenzo Librandi, Aug 10 2016

a(n) = Product_{i=1..9} (5^(n-i+1)-1)/(5^i-1), by definition. - Vincenzo Librandi, Aug 10 2016

Mathematica

Table[QBinomial[n, 9, 5], {n, 9, 20}] (* Vincenzo Librandi, Aug 10 2016 *)

Prog

(Sage) [gaussian_binomial(n, 9, 5) for n in range(9, 16)] # Zerinvary Lajos, May 25 2009
(Magma) r:=9; 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=9; 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: A184569 A210153 A144588 * A257195 A257188 A254988

Adjacent sequences: A022213 A022214 A022215 * A022217 A022218 A022219

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 10 2016

Status

approved