A009014 Expansion of E.g.f.: (1 + x)/(1 + x + x^2/2).

1, 0, -1, 3, -6, 0, 90, -630, 2520, 0, -113400, 1247400, -7484400, 0, 681080400, -10216206000, 81729648000, 0, -12504636144000, 237588086736000, -2375880867360000, 0, 548828480360160000, -12623055048283680000

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..450

Ghislain R. Franssens, On a Number Pyramid Related to the Binomial, Deleham, Eulerian, MacMahon and Stirling number triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.4.1.

Formula

E.g.f.: (1+x)/(1+x+x^2/2) = 1/cosh(log(1+x)).

a(n) = -n*a(n-1)-n*(n-1)/2*a(n-2), a(0)=1, a(1)=0.

From Peter Bala, Oct 05 2011: (Start)

a(n) = -n!*(((-1+i)/2)^(n+1) + ((-1-i)/2)^(n+1)) = -n!/sqrt(2)^(n-1)*cos(3*Pi*(n+1)/4).

a(n) = 1/2^n*A009769(n) = -n!/2^n*A009116(n+1).

a(n) = 2*(-1)^n*int {t = 0..inf} t^n*exp(-t)*cos(t). (End)

Maple

seq(coeff(series(factorial(n)*((1+x)/(1+x+x^2/2)), x, n+1), x, n), n=0..25); # Muniru A Asiru, Jul 21 2018

Mathematica

nn = 26; Range[0, nn]! CoefficientList[Series[1/Cosh[Log[1 + x]], {x, 0, nn}], x] (* T. D. Noe, Oct 05 2011 *)

Prog

(PARI) a(n)=-(2^-n)*n!*real((-1+I)^(n+1))
(PARI) x='x+O('x^30); Vec(serlaplace(1/cosh(log(1+x)))) \\ G. C. Greubel, Jul 21 2018

Crossrefs

Cf. A009116, A009769.

Sequence in context: A094674 A125287 A264813 * A009036 A021281 A034004

Adjacent sequences: A009011 A009012 A009013 * A009015 A009016 A009017

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Better description from Michael Somos

Status

approved