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A180875 Sum_{j>=1} j^n*2^j/binomial(2*j,j) = r_n*Pi/2 + s_n with integer r_n and s_n; sequence gives s_n. 7
1, 3, 11, 55, 355, 2807, 26259, 283623, 3473315, 47552791, 719718067, 11932268231, 215053088835, 4186305575415, 87534887434835, 46561960552921315, 1175204650272267479, 31357650670190565363, 881958890078887314567 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Lehmer's coefficients stemming from an inverse binomial coefficient series.

Left-hand side (portion of integer-only values not multiplied by Pi or Pi/2) on the table of Dyson et al.

LINKS

Table of n, a(n) for n=0..18.

F. J. Dyson, N. E. Frankel and M. L. Glasser, Lehmer's Second Interesting Series, arXiv:1009.4274 [math-ph], 2010-2011. (See Table IV)

F. J. Dyson, N. E. Frankel and M. L. Glasser, Lehmer's interesting series, Amer. Math. Monthly, 120 (2013), 116-130. (See Table 2)

FORMULA

a(0)=1; if n>=1, then a(n) = a(n-1) + 1 + Sum_{m=1..n} binomial(n,m)*a(n-m). - Detlef Meya, Jan 22 2018

MAPLE

f:=n->sum(j^n*(j!)^2*2^j/(2*j)!, j=1..infinity);

[seq(f(n), n=0..5)];

# which gives

# [1+1/2*Pi, 3+Pi, 11+7/2*Pi, 55+35/2*Pi, 355+113*Pi, 2807+1787/2*Pi]

CROSSREFS

The values of r_n give A014307.

Sequence in context: A001776 A261001 A207556 * A136104 A174627 A302147

Adjacent sequences:  A180872 A180873 A180874 * A180876 A180877 A180878

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, Sep 23 2010

EXTENSIONS

Attribution corrected by M. Lawrence Glasser, Sep 25 2010

Provided a better definition following a suggestion from Herb Conn. - N. J. A. Sloane, Feb 08 2011

STATUS

approved

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Last modified June 25 05:41 EDT 2019. Contains 324346 sequences. (Running on oeis4.)