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A187538
Alternating partial sums of the central Lah numbers (A187535).
11
1, 1, 35, 1165, 57635, 3752605, 303606755, 29378525725, 3309861378275, 425596952957725, 61508547037160675, 9870475998287280925, 1741469465493922587875, 335054673129161821412125, 69814770455871991714587875, 15662452678474786707959012125, 3764014801927115965888623387875
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k)*A187535(k).
(n+2)*a(n+2) - (16*n^2 + 47*n + 34)*a(n+1) - 4*(2*n+3)^2*a(n) = 0.
a(n) ~ 2^(4*n - 1/2) * n^(n - 1/2) / (sqrt(Pi) * exp(n)). - Vaclav Kotesovec, Mar 30 2018
MAPLE
A187538 := proc(n) add( (-1)^(n+k)*A187535(k), k=0..n) ; end proc:
seq(A187538(n), n=0..10) ; # R. J. Mathar, Mar 21 2011
MATHEMATICA
Table[(-1)^n + Sum[(-1)^(n-k)Binomial[2k-1, k-1](2k)!/k!, {k, 1, n}], {n, 0, 20}]
PROG
(Maxima) makelist((-1)^n+sum((-1)^(n-k)*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