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
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Dec 26 2000
STATUS
approved