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Search: id:A138773
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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 binom(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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1
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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
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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The polynomials Q[n](x) arise in a contact problem in elasticity theory.
Row sums yield A001803.
T(n,0)=A001790(n).
T(n,n)=A046161(n).
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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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FORMULA
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Q[n](x)=(2n+1)*Int((x+t^2)^n dt,t=0..sqrt(1-x))/sqrt(1-x). Q[n](x)=1+2nxQ[n-1](x)/(2n-1).
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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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Cf. A001803, A001790, A046161.
Sequence in context: A127074 A109617 A071373 this_sequence A132989 A114881 A082319
Adjacent sequences: A138770 A138771 A138772 this_sequence A138774 A138775 A138776
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 12 2008
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