A187538 - OEIS

%I #12 Feb 01 2019 02:34:32

%S 1,1,35,1165,57635,3752605,303606755,29378525725,3309861378275,

%T 425596952957725,61508547037160675,9870475998287280925,

%U 1741469465493922587875,335054673129161821412125,69814770455871991714587875,15662452678474786707959012125,3764014801927115965888623387875

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

%F a(n) = Sum_{k=0..n} (-1)^(n-k)*A187535(k).

%F (n+2)*a(n+2) - (16*n^2 + 47*n + 34)*a(n+1) - 4*(2*n+3)^2*a(n) = 0.

%F a(n) ~ 2^(4*n - 1/2) * n^(n - 1/2) / (sqrt(Pi) * exp(n)). - _Vaclav Kotesovec_, Mar 30 2018

%p A187538 := proc(n) add( (-1)^(n+k)*A187535(k),k=0..n) ; end proc:

%p seq(A187538(n),n=0..10) ; # _R. J. Mathar_, Mar 21 2011

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

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

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

%K nonn,easy

%O 0,3

%A _Emanuele Munarini_, Mar 11 2011