0,2

sum(n=1,inf,1/a(n))=Pi*sqrt(3)/9 - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 07 2002

Appears as diagonal in A003506. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 12 2006

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 78, (3.5.25).

A. J. van der Poorten, A proof that Euler missed...Apery's proof of the irrationality of zeta(3), Math. Intelligencer 1 (1978/1979), 195-203.

I. J. Zucker, On the series $ Sum\sp \infty\sb {k=1}(\sp{2k}\sb {\; k})\sp {-1}k\sp{-n}$ and related sums, J. Number Theory 20 (1985), no. 1, 92-102.

T. D. Noe, Table of n, a(n) for n=0..200

H. J. H. Tuenter, Walking into an absolute sum

Wadim Zudilin, An elementary proof of Apery's theorem

A005430 := n->n*binomial(2*n, n);

with(combinat):with(combstruct):a[0]:=0:for n from 1 to 30 do a[n]:=sum((count(Composition(n*2+1), size=n)), j=0..n) od: seq(a[n], n=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 03 2007

a:=n->add(binomial(2*n, n), k=1..n): seq(a(n), n=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 03 2007

a:=n->abs(sum((binomial(-n, n-3)), j=2..n)): seq(a(n), n=2..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 03 2007

(PARI) a(n)=-(-1)^n*real(polcoeff(serlaplace(x^2*besselh1(1, 2*x)), 2*n)) (from R. Stephan)

Cf. A002736, A005258, A005259, A005429, A005430. 1/beta(n, n+1) in A061928.

a(n) = A002011(n-1)/2 = 2 * A002457(n-1).

Cf. A001803.

Cf. A003506.

Sequence in context: A037133 A009618 A062478 this_sequence A094434 A001574 A074445

Adjacent sequences: A005427 A005428 A005429 this_sequence A005431 A005432 A005433

nonn,easy,nice

Simon Plouffe (plouffe(AT)math.uqam.ca)

More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 01 2000