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A138773
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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.
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0
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1, 1, 2, 3, 4, 8, 5, 6, 8, 16, 35, 40, 48, 64, 128, 63, 70, 80, 96, 128, 256, 231, 252, 280, 320, 384, 512, 1024, 429, 462, 504, 560, 640, 768, 1024, 2048, 6435, 6864, 7392, 8064, 8960, 10240, 12288, 16384, 32768, 12155, 12870, 13728, 14784, 16128, 17920, 20480
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OFFSET
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0,3
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COMMENTS
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The polynomials Q[n](x) arise in a contact problem in elasticity theory.
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REFERENCES
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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.
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LINKS
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FORMULA
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Q[n](x) = (2n+1)*(Integral_{t=0..sqrt(1-x)} (x+t^2)^n dt)/sqrt(1-x).
Q[n](x) = 1 + 2*n*x*Q[n-1](x)/(2n-1).
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EXAMPLE
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Triangle begins:
1,
1, 2,
3, 4, 8,
5, 6, 8, 16,
35, 40, 48, 64, 128,
63, 70, 80, 96, 128, 256,
...
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MAPLE
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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;
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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