A317410 Expansion of e.g.f. sec(x/(1 - x)).

1, 0, 1, 6, 41, 340, 3361, 38682, 508241, 7506504, 123108961, 2219822990, 43648348985, 929502984540, 21311829302401, 523455901397730, 13712375005949345, 381621247702458640, 11244620308691664961, 349715433597469496982, 11448372539225223596105, 393503844330372123056100, 14169282835811140260616801

Offset: 0

Author

Ilya Gutkovskiy, Jul 27 2018

Keywords

• nonn

Comments

Lah transform of the sequence 1, 0, 1, 0, 5, 0, 61, 0, 1385, ... (A000364 interspersed with zeros).

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000364, A317409.

Programs

Maple

a:=series(sec(x/(1 - x)), x=0, 23): seq(n!*coeff(a, x, n), n=0..22); # Paolo P. Lava, Mar 26 2019

Mathematica

nmax = 22; CoefficientList[Series[Sec[x/(1 - x)], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n - 1, k - 1] Abs[EulerE[k]] n!/k!, {k, 0, n}], {n, 0, 22}]

PARI

x = 'x + O('x^30); Vec(serlaplace(1/cos(x/(1 - x)))) \\ Michel Marcus, Jul 28 2018

Formula

E.g.f.: sec(x/(1 - x)).

a(n) ~ 4 * n! * (Pi+2)^(n-1) / Pi^(n+1). - Vaclav Kotesovec, Jul 28 2018