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A015197 Sum of Gaussian binomial coefficients for q=11.

%I A015197 #19 May 14 2019 09:38:35
%S A015197 1,2,14,268,19156,3961832,3092997464,7024809092848,60287817008722576,
%T A015197 1505950784990730735392,142158530752430089391520224,
%U A015197 39060769254069395008311334483648,40559566021977397260316290099710383936
%N A015197 Sum of Gaussian binomial coefficients for q=11.
%D A015197 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.
%D A015197 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.
%D A015197 M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
%H A015197 Vincenzo Librandi, <a href="/A015197/b015197.txt">Table of n, a(n) for n = 0..60</a>
%H A015197 Kent E. Morrison, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Morrison/morrison37.html">Integer Sequences and Matrices Over Finite Fields</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
%F A015197 a(n) = 2*a(n-1)+(11^(n-1)-1)*a(n-2), (Goldman + Rota, 1969). - _Vaclav Kotesovec_, Aug 21 2013
%F A015197 a(n) ~ c * 11^(n^2/4), where c = EllipticTheta[3,0,1/11]/QPochhammer[1/11,1/11] = 1.312069129398... if n is even and c = EllipticTheta[2,0,1/11]/QPochhammer[1/11,1/11] = 1.2291712170215... if n is odd. - _Vaclav Kotesovec_, Aug 21 2013
%t A015197 Total/@Table[QBinomial[n, m, 11], {n, 0, 20}, {m, 0, n}] (* _Vincenzo Librandi_, Nov 02 2012 *)
%t A015197 Flatten[{1,RecurrenceTable[{a[n]==2*a[n-1]+(11^(n-1)-1)*a[n-2],a[0]==1,a[1]==2},a,{n,1,15}]}] (* _Vaclav Kotesovec_, Aug 21 2013 *)
%Y A015197 Cf. A006116, A006117, A006118, A006119, A006120, A006121, A006122, A015195, A015196.
%Y A015197 Row sums of triangle A022175.
%K A015197 nonn
%O A015197 0,2
%A A015197 _N. J. A. Sloane_, _Olivier Gérard_