A187547 L(n)H(n+1), product of the central Lah number L(n) and the harmonic number H(n).

1, 3, 66, 2500, 134260, 9335088, 796938912, 80671795776, 9446603680800, 1256254443100800, 187033518310129920, 30821040496874234880, 5569495264653352381440, 1095113648992295923200000, 232773183612995427763200000, 53186532693832607435089920000

Offset: 0

Author

Emanuele Munarini, Mar 11 2011

Keywords

• nonn
• easy

Crossrefs

Cf. A187536, A008297, A111596, A187536, A187538, A187539, A187540, A187542, A187543, A187544, A187545, A187546, A187548.

Programs

Maple

a := n -> if n=0 then 1 else binomial(2*n-1,n-1)*(2*n)!/n! fi;
seq(a(n)*sum(1/k,k=1..n+1),n=0..12);

Mathematica

a[n_] := If[n == 0, 1, Binomial[2n - 1, n - 1](2n)!/n!]
Table[a[n]HarmonicNumber[n + 1], {n, 0, 20}]

Maxima

a(n):= if n=0 then 1 else binomial(2*n-1,n-1)*(2*n)!/n!;
makelist(a(n)*sum(1/k,k,1,n+1),n,0,12);

Formula

Recurrence:

(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.