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%I #7 Nov 12 2019 04:18:01
%S 1,1,2,3,4,8,5,6,8,16,35,40,48,64,128,63,70,80,96,128,256,231,252,280,
%T 320,384,512,1024,429,462,504,560,640,768,1024,2048,6435,6864,7392,
%U 8064,8960,10240,12288,16384,32768,12155,12870,13728,14784,16128,17920,20480
%N Triangle read by rows: T(n,k) is the coefficient of x^k in the polynomial P[n](x) = b(n)Q[n](x), where b(n) = numerator of binomial(2n,n)/2^n = A001790(n) and Q[n](x) = F(-n,1; 1/2-n; x) (hypergeometric function); 0 <= k <= n.
%C The polynomials Q[n](x) arise in a contact problem in elasticity theory.
%C Row sums yield A001803.
%C T(n,0) = A001790(n).
%C T(n,n) = A046161(n).
%D E. G. Deich (E. Deutsch), On an axially symmetric contact problem for a non-plane stamp with a circular cross-section (in Russian), Prikl. Mat. Mekh., 26, No. 5, 1962, 931-934.
%F Q[n](x) = (2n+1)*(Integral_{t=0..sqrt(1-x)} (x+t^2)^n dt)/sqrt(1-x).
%F Q[n](x) = 1 + 2*n*x*Q[n-1](x)/(2n-1).
%e Triangle begins:
%e 1,
%e 1, 2,
%e 3, 4, 8,
%e 5, 6, 8, 16,
%e 35, 40, 48, 64, 128,
%e 63, 70, 80, 96, 128, 256,
%e ...
%p p:=proc(n) options operator, arrow: numer(simplify(hypergeom([ -n, 1], [1/2-n], x))) end proc: for n from 0 to 9 do P[n]:=p(n) end do: for n from 0 to 9 do seq(coeff(P[n],x,k),k=0..n) end do;
%Y Cf. A001803, A001790, A046161.
%K nonn,tabl
%O 0,3
%A _Emeric Deutsch_, Apr 12 2008
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