A022219 Gaussian binomial coefficients [ n,12 ] for q = 5.

1, 305175781, 77610214474995931, 19100611156944225555440431, 4670708278954101902438990598678556, 1140674654304411569828223908172341508228556, 278502847205686141650283863407927164540769884103556

Offset

12,2

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 = 12..130

Formula

G.f.: x^12/((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)*(1-48828125*x)*(1-244140625*x)). - Vincenzo Librandi, Aug 10 2016

a(n) = Product_{i=1..12} (5^(n-i+1)-1)/(5^i-1), by definition. - Vincenzo Librandi, Aug 10 2016

Mathematica

Table[QBinomial[n, 12, 5], {n, 12, 20}] (* Vincenzo Librandi, Aug 10 2016 *)

Prog

(Sage) [gaussian_binomial(n, 12, 5) for n in range(12, 18)] # Zerinvary Lajos, May 28 2009
(Magma) r:=12; 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=12; 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: A183800 A289908 A182990 * A285433 A104965 A251807

Adjacent sequences: A022216 A022217 A022218 * A022220 A022221 A022222

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 10 2016

Status

approved