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A187536
Partial sums of the central Lah numbers (A187535).
11
1, 3, 39, 1239, 60039, 3870279, 311229639, 29993362119, 3369233266119, 432276047602119, 62366420037720519, 9994350965362162119, 1761334292457572030919, 338557476887113316030919, 70488382605888266852030919, 15802755831536546966525630919
OFFSET
0,2
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);
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Mar 11 2011
STATUS
approved