A015422 - OEIS

A015422

Gaussian binomial coefficient [ n,11 ] for q=-13.

1, -1664148937320, 3000174326048697741925710, -5374347381421937558314402513609688760, 9632029764916740618771445568833182996026908640493, -17262095767026556801586191040816999767731925288888540910160480

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OFFSET

11,2

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 = 11..90

Index entries related to Gaussian binomial coefficients.

FORMULA

a(n) = Product_{i=1..11} ((-13)^(n-i+1)-1)/((-13)^i-1). - M. F. Hasler, Nov 03 2012

MATHEMATICA

Table[QBinomial[n, 11, -13], {n, 11, 20}] (* Vincenzo Librandi, Nov 06 2012 *)

PROG

(Sage) [gaussian_binomial(n, 11, -13) for n in range(11, 16)] # Zerinvary Lajos, May 28 2009

(PARI) A015422(n, r=11, q=-13)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012

(Magma) r:=11; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Nov 06 2012

CROSSREFS

Cf. Gaussian binomial coefficients [n,r] for q=-13: A015265 (r=2), A015286 (r=3), A015303 (r=4), A015321 (r=5), A015337 (r=6), A015355 (r=7), A015370 (r=8), A015385 (r=9), A015402 (r=10), A015438 (r=12). - M. F. Hasler, Nov 03 2012

Sequence in context: A320943 A248892 A172799 * A289148 A282182 A017543

Adjacent sequences: A015419 A015420 A015421 * A015423 A015424 A015425

KEYWORD

sign,easy

AUTHOR

Olivier Gérard

STATUS

approved