OFFSET
0,3
COMMENTS
Lah transform of the sequence 0, 1, 0, -1, 0, 1, 0, -1, ...
LINKS
N. J. A. Sloane, Transforms
FORMULA
a(n) = Sum_{k=1..floor((n+1)/2)} (-1)^(k+1)*binomial(n-1,2*k-2)*n!/(2*k-1)!.
MAPLE
a:=series(sin(x/(1 - x)), x=0, 22): seq(n!*coeff(a, x, n), n=0..21); # Paolo P. Lava, Mar 26 2019
MATHEMATICA
nmax = 22; CoefficientList[Series[Sin[x/(1 - x)], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^(k + 1) Binomial[n - 1, 2 k - 2] n!/(2 k - 1)!, {k, Floor[(n + 1)/2]}], {n, 0, 22}]
Join[{0}, Table[n! HypergeometricPFQ[{1/2 - n/2, 1 - n/2}, {1/2, 1, 3/2}, -1/4], {n, 22}]]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jul 27 2018
STATUS
approved