A187547 - OEIS

%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