A015394 Gaussian binomial coefficient [ n,10 ] for q=-8.

1, 954437177, 1041086085394771065, 1115678612484825190455949945, 1198243328242032079710778546865654393, 1286564714023293732070008866290952083995937401, 1381443612518576172240265744739493702803061753684478585

Offset

10,2

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 = 10..120

Formula

a(n) = Product_{i=1..10} ((-8)^(n-i+1)-1)/((-8)^i-1) (by definition). - Vincenzo Librandi, Nov 04 2012

Mathematica

Table[QBinomial[n, 10, -8], {n, 10, 20}] (* Vincenzo Librandi, Nov 04 2012 *)

Prog

(Sage) [gaussian_binomial(n, 10, -8) for n in range(10, 16)] # Zerinvary Lajos, May 25 2009
(Magma) r:=10; q:=-8; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..25]]; // Vincenzo Librandi, Nov 04 2012

Crossrefs

Cf. Gaussian binomial coefficients [n, 10] for q = -2..-13: A015386, A015388, A015390, A015391, A015392, A015393, A015397, A015398, A015399, A015401, A015402. - Vincenzo Librandi, Nov 04 2012

Sequence in context: A186805 A122532 A172605 * A114261 A321489 A168436

Adjacent sequences: A015391 A015392 A015393 * A015395 A015396 A015397

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved