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A022231
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Gaussian binomial coefficients [ n,2 ] for q = 7.
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2
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1, 57, 2850, 140050, 6865251, 336416907, 16484565700, 807744680100, 39579496050501, 1939395353553757, 95030372653688550, 4656488262337620150, 228167924870691555751, 11180228318776923410607, 547831187620860507371400
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OFFSET
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2,2
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LINKS
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FORMULA
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G.f.: x^2/((1-x)*(1-7*x)*(1-49*x)).
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
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MAPLE
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seq((7^(n+1)-1)*(7^(n+2)-1)/288, n=0..30); # Robert Israel, Dec 16 2014
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MATHEMATICA
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a[n_Integer/; n>=0]:=(7^(n+1)-1)*(7^(n+2)-1)/288 (* Todd Silvestri, Dec 16 2014 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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