A317409 Expansion of e.g.f. cos(x/(1 - x)).

1, 0, -1, -6, -35, -220, -1501, -10962, -83495, -632952, -4260601, -13852190, 355180981, 12991115436, 320077652075, 7153866992790, 155785273182001, 3395838000334352, 75000970329466895, 1687941779356532682, 38803334491247820301, 911633573138881234740, 21870615120012355726259

Offset

0,4

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 0..446

N. J. A. Sloane, Transforms

Formula

a(n) = Sum_{k=0..floor(n/2)} (-1)^k*binomial(n-1,2*k-1)*n!/(2*k)!.

-2*(2*n + 3)*(n + 2)*(n + 1)*a(n + 1) + (6*n^2 + 24*n + 25)*a(n + 2) - 2*(2*n + 5)*a(n + 3) + a(n + 4) + n*(n + 2)*(n + 1)^2*a(n)=0. - Robert Israel, Mar 26 2019

Maple

a:=series(cos(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[Cos[x/(1 - x)], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^k Binomial[n - 1, 2 k - 1] n!/(2 k)!, {k, 0, Floor[n/2]}], {n, 0, 22}]
Join[{1}, Table[(1 - n) n! HypergeometricPFQ[{1 - n/2, 3/2 - n/2}, {3/2, 3/2, 2}, -1/4]/2, {n, 22}]]

Prog

(PARI) my(x='x + O('x^25)); Vec(serlaplace(cos(x/(1 - x)))) \\ Michel Marcus, Mar 26 2019

Crossrefs

Cf. A056594, A088312, A219613, A317406, A317410.

Sequence in context: A117671 A354136 A370323 * A354324 A213452 A357834

Adjacent sequences: A317406 A317407 A317408 * A317410 A317411 A317412

Keyword

sign

Author

Ilya Gutkovskiy, Jul 27 2018

Status

approved