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A278390 Triangle T(n,k) read by rows: the number of independent sets of size k in the 132 core of size n.

%I A278390 #17 Sep 28 2019 12:30:28
%S A278390 1,1,1,1,3,3,1,6,14,16,1,10,40,85,105,1,15,90,295,594,771,1,21,175,
%T A278390 805,2331,4529,6083,1,28,308,1876,7280,19348,36644,50464,1,36,504,
%U A278390 3906,19404,66780,166608,309537,434493,1,45,780,7470,45990,197484,621180,1476135,2701610,3849715
%N A278390 Triangle T(n,k) read by rows: the number of independent sets of size k in the 132 core of size n.
%H A278390 C. Bean, M. Tannock, H. Ulfarsson, <a href="http://arxiv.org/abs/1512.08155">Pattern avoiding permutations and independent sets in graphs</a>, arXiv:1512.08155 [math.CO], 2015, Theorem 3.5.
%F A278390 The bivariate g.f. G(x,y) satisfies G = 1+x*G+x*y*G^2/(1-y*(G-1)).
%F A278390 n*T(n,k) = Sum_{j=0..n-1} binomial(n,k-j)*binomial(n,j+1)*binomial(n-1+j,n-1).
%e A278390 1;
%e A278390 1,  1;
%e A278390 1,  3,   3;
%e A278390 1,  6,  14,   16;
%e A278390 1, 10,  40,   85,   105;
%e A278390 1, 15,  90,  295,   594,   771;
%e A278390 1, 21, 175,  805,  2331,  4529,   6083;
%e A278390 1, 28, 308, 1876,  7280, 19348,  36644,  50464;
%e A278390 1, 36, 504, 3906, 19404, 66780, 166608, 309537, 434493;
%t A278390 T[n_, k_] := Binomial[n-1, k] HypergeometricPFQ[{-k, 2-n, n-1}, {2, n-k}, 1];
%t A278390 Table[T[n, k], {n, 1, 10}, {k, 0, n-1}] (* _Jean-François Alcover_, Sep 28 2019 *)
%K A278390 easy,tabl,nonn
%O A278390 1,5
%A A278390 _R. J. Mathar_, Nov 20 2016