A187538 Alternating partial sums of the central Lah numbers (A187535).

1, 1, 35, 1165, 57635, 3752605, 303606755, 29378525725, 3309861378275, 425596952957725, 61508547037160675, 9870475998287280925, 1741469465493922587875, 335054673129161821412125, 69814770455871991714587875, 15662452678474786707959012125, 3764014801927115965888623387875

Offset: 0

Author

Emanuele Munarini, Mar 11 2011

Keywords

• nonn
• easy

Crossrefs

Cf. A187536, A008297, A111596, A187536, A187539, A187540, A187542 - A187548.

Programs

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}]

Maxima

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

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