A022218 Gaussian binomial coefficients [ n,11 ] for q = 5.

1, 61035156, 3104408566792806, 152804888634672088643556, 7473133215765585192791624069181, 365015887882785053079719041834672291056, 17824182148160735190135826789101008407579416056, 870332534209370628368397575515105530919233947896291056

Offset

11,2

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 = 11..140

Formula

G.f.: x^11/((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)). - Vincenzo Librandi, Aug 10 2016

a(n) = Product_{i=1..11} (5^(n-i+1)-1)/(5^i-1), by definition. - Vincenzo Librandi, Aug 10 2016

Mathematica

Table[QBinomial[n, 11, 5], {n, 11, 20}] (* Vincenzo Librandi, Aug 10 2016 *)

Prog

(Sage) [gaussian_binomial(n, 11, 5) for n in range(11, 19)] # Zerinvary Lajos, May 28 2009
(Magma)  r:=11; 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=11; 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: A172584 A210354 A309062 * A059001 A059003 A104931

Adjacent sequences: A022215 A022216 A022217 * A022219 A022220 A022221

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Offset changed by Vincenzo Librandi, Aug 10 2016

Status

approved