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 A181334 Let f(n) = Sum_{j>=1} j^n/binomial(2*j,j) = r_n*Pi*sqrt(3)/3^{t_n} + s_n/3; sequence gives r_n. 3
 2, 2, 10, 74, 238, 938, 13130, 23594, 1298462, 26637166, 201403930, 5005052234, 135226271914, 1315508114654, 13747435592810, 153590068548062, 202980764290906, 69141791857625242, 2766595825017102650, 38897014541363246798, 1724835471991750464238, 80219728936311383557694 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS F. J. Dyson, N. E. Frankel and M. L. Glasser, Lehmer's Second Interesting Series, arXiv:1009.4274 [math-ph], 2010-2011. F. J. Dyson, N. E. Frankel and M. L. Glasser, Lehmer's interesting series, Amer. Math. Monthly, 120 (2013), 116-130. MAPLE A181334:=proc(n)local j, x, y, z, tol; x:=0; y:=1; j:=1; tol:=100; #increase tol for very large value of n (n>50) or this may become inaccurate while y>10^(-tol) do y:=j^n/binomial(2*j, j); x:=x+y; j:=j+1; od: return numer(convert(evalf(((x-A098830(n)/3)/(Pi*sqrt(3)))), rational, tol-1)); end: # Nathaniel Johnston, Apr 07 2011 MATHEMATICA f[n_] := Sum[j^n/Binomial[2*j, j], {j, 1, Infinity}]; a[n_] := Expand[ FunctionExpand[ f[n] ] ][[2, 1]] // Numerator; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Nov 24 2017 *) CROSSREFS Cf. A098830 (s_n), A185585 (t_n), A181374, A180875, A014307. Sequence in context: A052647 A326983 A232974 * A032034 A002250 A304642 Adjacent sequences:  A181331 A181332 A181333 * A181335 A181336 A181337 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 09 2011, following a suggestion from Herb Conn EXTENSIONS a(11)-a(21) from Nathaniel Johnston, Apr 07 2011 STATUS approved

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Last modified October 15 13:06 EDT 2019. Contains 328030 sequences. (Running on oeis4.)