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A015369 Gaussian binomial coefficient [ n,8 ] for q=-12. 13
1, 396906181, 171855836163195541, 73852125402551558141191381, 31756593605318274408653251348629973, 13654699102424414895934644240803700147539413, 5871272644707452307243912611380074655778555267227093 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,2

REFERENCES

J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.

M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 8..100

FORMULA

a(n) = Product_{i=1..8} ((-12)^(n-i+1)-1)/((-12)^i-1). - M. F. Hasler, Nov 03 2012

MAPLE

A015369:=n->mul(((-12)^(n-i+1)-1)/((-12)^i-1), i=1..8): seq(A015369(n), n=8..20); # Wesley Ivan Hurt, Jan 29 2017

MATHEMATICA

Table[QBinomial[n, 8, -12], {n, 8, 14}] (* Vincenzo Librandi, Nov 03 2012 *)

PROG

(Sage) [gaussian_binomial(n, 8, -12) for n in xrange(8, 14)] # Zerinvary Lajos, May 24 2009

(MAGMA) r:=8; q:=-12; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..18]]; // Vincenzo Librandi, Nov 03 2012

(PARI) A015369(n, r=8, q=-12)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

CROSSREFS

Cf. Gaussian binomial coefficients [n,8] for q=-2..-13: A015356, A015357, A015359, A015360, A015361, A015363, A015364, A015365, A015367, A015368, A015370. - M. F. Hasler, Nov 03 2012

Sequence in context: A058125 A175280 A271022 * A321138 A103773 A172602

Adjacent sequences:  A015366 A015367 A015368 * A015370 A015371 A015372

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified March 26 12:27 EDT 2019. Contains 321497 sequences. (Running on oeis4.)