A187536 Partial sums of the central Lah numbers (A187535).

1, 3, 39, 1239, 60039, 3870279, 311229639, 29993362119, 3369233266119, 432276047602119, 62366420037720519, 9994350965362162119, 1761334292457572030919, 338557476887113316030919, 70488382605888266852030919, 15802755831536546966525630919

Offset: 0

Author

Emanuele Munarini, Mar 11 2011

Keywords

• nonn
• easy

Crossrefs

Cf. A187535, A008297, A111596, A187538 - A187540, A187542 - A187548.

Programs

Maple

A187536 := proc(n) add(A187535(i),i=0..n) ; end proc:
seq(A187536(n),n=0..10) ; # R. J. Mathar, Mar 20 2011

Mathematica

Table[1 + Sum[Binomial[2k-1,k-1](2k)!/k!, {k, 1, n}], {n, 0, 20}]

Maxima

makelist(1+sum(binomial(2*k-1,k-1)*(2*k)!/k!,k,1,n),n,0,12);

Formula

a(n) = 1 + Sum_{k=0..n} binomial(2k-1,k-1)*(2k)!/k!.

(n+2)*a(n+2) - (16n^2 + 49n +3 8)*a(n+1) + 4 *(2n+3)^2*a(n) = 0.

Asymptotically a(n) ~ 2^(4n)n^n exp(-n)/sqrt(2n*pi).