A058607 a(n) = (1 + 1/2 + 1/3 + ... + 1/n)*(2n-1)!/(n-1)!.

1, 9, 110, 1750, 34524, 814968, 22424688, 705173040, 24956062560, 981852505920, 42517741069440, 2009786716304640, 102980287835712000, 5685838994441088000, 336540101841974016000, 21258495023757610752000, 1427473447879197261312000, 101537097118783918986240000, 7626891980577579870504960000

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..365

Hongwei Chen, Interesting Series Associated with Central Binomial Coefficients, Catalan Numbers and Harmonic Numbers, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.5, p. 3.

Formula

E.g.f.: log((1 + 1/sqrt(1-4*x))/2)/sqrt(1-4*x).

a(n) = n!*Sum_{k=1..n} (binomial(2*n,n-k)/k). - Vladimir Kruchinin, Mar 31 2016

a(n) = 2*(2*n-1)*a(n-1)+binomial(2*n-1,n)*(n-1)!, a(1)=1. - Vladimir Kruchinin, Jun 11 2016

a(n) = hypergeom([1,1,1-n],[2,n+2],-1)*n*(2*n)!/(n+1)!. - Peter Luschny, Jun 11 2016

Maple

A058607 := n -> hypergeom([1, 1, 1-n], [2, n+2], -1)*n*(2*n)!/(n+1)!:
seq(simplify(A058607(n)), n=1..19); # Peter Luschny, Jun 11 2016

Mathematica

Rest[CoefficientList[Series[Log[(1 + 1/Sqrt[1 - 4 x])/2]/Sqrt[1 - 4 x], {x, 0, 20}], x] Range[0, 20]!] (* Vaclav Kotesovec, Apr 01 2016 *)
a[n_] := HarmonicNumber[n] Pochhammer[n, n];
Array[a, 20] (* Jean-François Alcover, Jun 13 2016 *)

Prog

(Maxima) a(n):=n!*sum(binomial(2*n, n-k)/k, k, 1, n); /* Vladimir Kruchinin, Mar 31 2016 */
(PARI) a(n) = n!*sum(k=1, n, binomial(2*n, n-k)/k); \\ Michel Marcus, Mar 31 2016
(PARI) x='x+O('x^44); Vec(serlaplace(log((1 + 1/sqrt(1-4*x))/2)/sqrt(1-4*x))) \\ Joerg Arndt, Apr 01 2016

Crossrefs

Sequence in context: A053912 A053894 A053904 * A298835 A082723 A352384

Adjacent sequences: A058604 A058605 A058606 * A058608 A058609 A058610

Keyword

easy,nonn

Author

Leroy Quet, Dec 26 2000

Status

approved