OFFSET
0,3
COMMENTS
REFERENCES
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.
FORMULA
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).
EXAMPLE
Triangle begins:
1,
1, 2,
3, 4, 8,
5, 6, 8, 16,
35, 40, 48, 64, 128,
63, 70, 80, 96, 128, 256,
...
MAPLE
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;
MATHEMATICA
b[n_] := Numerator[Binomial[2n, n]/2^n];
Q[n_][x_] := HypergeometricPFQ[{-n, 1}, {1/2 - n}, x];
T[n_, k_] := Coefficient[b[n]*Q[n][x], x, k];
Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 23 2024 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Apr 12 2008
STATUS
approved