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

0,2

Links

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

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).

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}]

Prog

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

Crossrefs

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

Sequence in context: A274573 A278750 A082159 * A369945 A084881 A193122

Adjacent sequences: A187533 A187534 A187535 * A187537 A187538 A187539

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 11 2011

Status

approved