A187542 Convolutions of the central Lah numbers (A187535).

1, 4, 76, 2544, 123696, 7942080, 635633280, 61009159680, 6831940227840, 874493448514560, 125946241018214400, 20156433977646489600, 3548609812373223628800, 681555522002874494976000, 141810253720479017017344000

Offset: 0

Author

Emanuele Munarini, Mar 11 2011

Keywords

• nonn
• easy

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A187536, A008297, A111596, A187536, A187538, A187539, A187540, A187543, A187544, A187545, A187546, A187547, A187548.

Programs

Maple

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

Mathematica

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

Maxima

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

Formula

a(n) = sum(L(k)L(n-k),k=0..n), where L(n) is a central Lah number.

a(n) ~ n! * 16^n / (Pi*n). - Vaclav Kotesovec, Oct 06 2019