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

0,2

Links

Table of n, a(n) for n=0..15.

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.

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}]

Prog

(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);

Crossrefs

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

Sequence in context: A157543 A368596 A157984 * A157554 A185053 A165655

Adjacent sequences: A187544 A187545 A187546 * A187548 A187549 A187550

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 11 2011

Status

approved