A187548 Alternating partial sums of L(n)*H(n+1), product of central Lah number L(n) and Harmonic number H(n+1).

1, 2, 64, 2436, 131824, 9203264, 787735648, 79884060128, 9366719620672, 1246887723480128, 185786630586649792, 30635253866287585088, 5538860010787064796352, 1089574788981508858403648, 231683608824013918904796352, 52954849085008593516185123648

Offset: 0

Author

Emanuele Munarini, Mar 11 2011

Keywords

• nonn
• easy

Crossrefs

Cf. A187535, A001008, A187547.

Programs

Maple

H := proc(n) add(1/i,i=1..n) ; end proc:
A187535 := proc(n) if n=0 then 1; else binomial(2*n-1, n-1)*(2*n)!/n! end if; end proc:
A187547 := proc(n) H(n+1)*A187535(n) ; end proc:
A187548 := proc(n) add( A187547(k)*(-1)^(n-k),k=0..n) ; end proc:
seq(A187548(n),n=0..20) ; # R. J. Mathar, Mar 24 2011

Mathematica

Table[Sum[(-1)^n+(-1)^(n-k)Binomial[2k-1,k-1](2k)!/k!HarmonicNumber[k+1],{k,1,n}],{n,0,12}]

Maxima

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

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k)*A187547(k).