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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

Table of n, a(n) for n=0..21.

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-Fran├žois Alcover, Nov 24 2017 *)

CROSSREFS

Cf. A098830 (s_n), A185585 (t_n), A181374, A180875, A014307.

Sequence in context: A059494 A052647 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 March 26 06:55 EDT 2019. Contains 321481 sequences. (Running on oeis4.)