A317406 Expansion of e.g.f. sin(x/(1 - x)).

0, 1, 2, 5, 12, 1, -450, -6931, -89096, -1120895, -14394150, -191263051, -2638282812, -37716883775, -556075744042, -8385570334051, -127637336779920, -1916072623603199, -27033275598036174, -311878728377256475, -918069644450841860, 120594465496571606401, 6362190374664242284782

Offset: 0

Author

Ilya Gutkovskiy, Jul 27 2018

Keywords

• sign

Comments

Lah transform of the sequence 0, 1, 0, -1, 0, 1, 0, -1, ...

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A088313, A219613, A317409.

Programs

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}]]

Formula

a(n) = Sum_{k=1..floor((n+1)/2)} (-1)^(k+1)*binomial(n-1,2*k-2)*n!/(2*k-1)!.