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A187548
Alternating partial sums of L(n)*H(n+1), product of central Lah number L(n) and Harmonic number H(n+1).
12
1, 2, 64, 2436, 131824, 9203264, 787735648, 79884060128, 9366719620672, 1246887723480128, 185786630586649792, 30635253866287585088, 5538860010787064796352, 1089574788981508858403648, 231683608824013918904796352, 52954849085008593516185123648
OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k)*A187547(k).
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}]
PROG
(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);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Mar 11 2011
STATUS
approved