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A022231 Gaussian binomial coefficients [ n,2 ] for q = 7. 2
1, 57, 2850, 140050, 6865251, 336416907, 16484565700, 807744680100, 39579496050501, 1939395353553757, 95030372653688550, 4656488262337620150, 228167924870691555751, 11180228318776923410607, 547831187620860507371400 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Todd Silvestri and Vincenzo Librandi, Table of n, a(n) for n = 2..200 (first 591 terms from Todd Silvestri )

FORMULA

G.f.: x^2/((1-x)*(1-7*x)*(1-49*x)).

a(n) = (7^(n+1)-1)*(7^(n+2)-1)/288. - Todd Silvestri, Dec 16 2014

E.g.f.: (343*exp(49*x)-56*exp(7*x)+exp(x))/288. - Robert Israel, Dec 16 2014

a(n+3) = 57*a(n+2) - 399*a(n+1) + 343*a(n). - Robert Israel, Dec 16 2014

MAPLE

seq((7^(n+1)-1)*(7^(n+2)-1)/288, n=0..30); # Robert Israel, Dec 16 2014

MATHEMATICA

a[n_Integer/; n>=0]:=(7^(n+1)-1)*(7^(n+2)-1)/288 (* Todd Silvestri, Dec 16 2014 *)

Table[QBinomial[n, 2, 7], {n, 2, 20}] (* Vincenzo Librandi, Aug 12 2016 *)

PROG

(Sage) [gaussian_binomial(n, 2, 7) for n in range(2, 17)] # Zerinvary Lajos, May 28 2009

(PARI) Vec(1/((1-x)*(1-7*x)*(1-49*x)) + O(x^30)) \\ Michel Marcus, Dec 16 2014

(PARI) r=2; q=7; for(n=r, 30, print1(prod(j=1, r, (1-q^(n-j+1))/(1-q^j)), ", ")) \\ G. C. Greubel, Jun 13 2018

(PARI) lista(nn, na=2, q=7) = qp=matpascal(nn+q, q); vector(nn, n, qp[n+na, n]); \\ Michel Marcus, Jun 13 2018

(MAGMA) r:=2; q:=7; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 12 2016

CROSSREFS

Sequence in context: A285238 A011812 A226848 * A239823 A012058 A122533

Adjacent sequences:  A022228 A022229 A022230 * A022232 A022233 A022234

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 November 26 23:41 EST 2020. Contains 338670 sequences. (Running on oeis4.)