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A117852 Mirror image of A098473 formatted as a triangular array.

%I A117852 #22 Sep 24 2018 16:53:14
%S A117852 1,2,1,6,4,1,20,18,6,1,70,80,36,8,1,252,350,200,60,10,1,924,1512,1050,
%T A117852 400,90,12,1,3432,6468,5292,2450,700,126,14,1,12870,27456,25872,14112,
%U A117852 4900,1120,168,16,1,48620,115830,123552,77616,31752,8820,1680,216,18,1
%N A117852 Mirror image of A098473 formatted as a triangular array.
%H A117852 G. C. Greubel, <a href="/A117852/b117852.txt">Table of n, a(n) for the first 100 rows, flattened</a>
%F A117852 Sum_{k=0..n} T(n,k)*x^k = A126869(n), A002426(n), A000984(n), A026375(n), A081671(n), A098409(n), A098410(n) for x = -2, -1, 0, 1, 2, 3, 4 respectively. - _Philippe Deléham_, Sep 28 2007
%F A117852 T(n,k) = binomial(n,k)*A000984(n-k). - _Philippe Deléham_, Dec 12 2009
%F A117852 O.g.f.:  1/sqrt( (1 - x*t)*(1 - (x + 4)*t) ) = 1 + (2 + x)*t + (6 + 4*x + x^2)*t^2 + .... - _Peter Bala_, Nov 10 2013
%e A117852 Triangle begins:
%e A117852     1;
%e A117852     2,   1;
%e A117852     6,   4,   1;
%e A117852    20,  18,   6,   1;
%e A117852    70,  80,  36,   8,   1;
%e A117852   252, 350, 200,  60,  10,   1;
%e A117852   ...
%p A117852 c:=n->binomial(2*n, n): T:=proc(n, k) if k<=n then binomial(n, k)*c(n-k) else 0 fi end: for n from 0 to 10 do seq(T(n, k), k=0..n) od; #
%t A117852 Table[ Binomial[n, k]*Binomial[2*n - 2*k, n - k], {n,0,10}, {k,0,n} ] // Flatten (* _G. C. Greubel_, Mar 07 2017 *)
%Y A117852 Cf. A098473.
%K A117852 nonn,tabl
%O A117852 0,2
%A A117852 Farkas Janos Smile (smile_farkasjanos(AT)yahoo.com.au), Dec 21 2006
%E A117852 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jun 12 2007