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A181374 Let f(n) = sum(j^n*3^j/binomial(2*j,j),j=1..infinity) = r_n*Pi/sqrt(3) + s_n; sequence gives s_n. 3
3, 18, 156, 1890, 29496, 563094, 12709956, 331109658, 9777612432 (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]}][[2]];

Table[s = a[n]; Print[s]; s, {n, 0, 8}] (* Jean-François Alcover, Sep 05 2018 *)

CROSSREFS

Cf. A185672 (r_n), A180875 and A014307 (2^j rather than 3^j).

Sequence in context: A107888 A293491 A138274 * A060913 A246523 A246529

Adjacent sequences:  A181371 A181372 A181373 * A181375 A181376 A181377

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 May 22 18:53 EDT 2019. Contains 323481 sequences. (Running on oeis4.)