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A185672 Let f(n) = sum(j^n*3^j/binomial(2*j,j),j=1..infinity) = r_n*Pi/sqrt(3) + s_n; sequence gives r_n. 1
4, 20, 172, 2084, 32524, 620900, 14014732, 365100644, 10781360524 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..8.

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.

MATHEMATICA

f[n_] := Sum[j^n*3^j/Binomial[2*j, j], {j, 1, Infinity}];

a[n_] := FindIntegerNullVector[{Pi/Sqrt[3], 1, N[-f[n], 20]}][[1]];

Table[r = a[n]; Print[r]; r, {n, 0, 8}] (* Jean-Fran├žois Alcover, Sep 05 2018 *)

CROSSREFS

Cf. A181374 (s_n), A180875 and A014307 (2^j rather than 3^j).

Sequence in context: A065526 A032333 A068965 * A210438 A054474 A213144

Adjacent sequences:  A185669 A185670 A185671 * A185673 A185674 A185675

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Feb 09 2011, following a suggestion from Herb Conn

STATUS

approved

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Last modified November 13 10:29 EST 2019. Contains 329093 sequences. (Running on oeis4.)