|
%I #7 Mar 30 2012 18:55:29
%S 1,3,66,2500,134260,9335088,796938912,80671795776,9446603680800,
%T 1256254443100800,187033518310129920,30821040496874234880,
%U 5569495264653352381440,1095113648992295923200000,232773183612995427763200000,53186532693832607435089920000
%N L(n)H(n+1), product of the central Lah number L(n) and the harmonic number H(n).
%F Recurrence:
%F (n+3)(n+2)(n+1)a(n+2)-4(2n+3)^2(2n+5)(n+1)a(n+1)+16(2n+3)^2(2n+1)^2(n+2)a(n)-144delta(n,0)=0.
%p a := n -> if n=0 then 1 else binomial(2*n-1,n-1)*(2*n)!/n! fi;
%p seq(a(n)*sum(1/k,k=1..n+1),n=0..12);
%t a[n_] := If[n == 0, 1, Binomial[2n - 1, n - 1](2n)!/n!]
%t Table[a[n]HarmonicNumber[n + 1], {n, 0, 20}]
%o (Maxima) a(n):= if n=0 then 1 else binomial(2*n-1,n-1)*(2*n)!/n!;
%o makelist(a(n)*sum(1/k,k,1,n+1),n,0,12);
%Y Cf. A187536, A008297, A111596, A187536, A187538, A187539, A187540, A187542, A187543, A187544, A187545, A187546, A187548.
%K nonn,easy
%O 0,2
%A _Emanuele Munarini_, Mar 11 2011
|
