OFFSET
0,2
REFERENCES
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.25(b).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: ((1+x)/(1-x))^(1/4) * exp(x*(3 + x)/2).
a(n) ~ n! * 2^(-1/4)*Gamma(3/4)*exp(2)/(Pi*n^(3/4)). - Vaclav Kotesovec, Aug 13 2013
Recurrence: 2*a(n) = 4*a(n-1) + 2*(n-1)^2*a(n-2) - 3*(n-2)*(n-1)*a(n-3) - 2*(n-3)*(n-2)*(n-1)*a(n-4). - Vaclav Kotesovec, Aug 13 2013
MATHEMATICA
max = 30; f[x_]:= ((1+x)/(1-x))^(1/4)*Exp[x*(3+x)/2]; CoefficientList[ Series[f[x], {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Nov 30 2011 *)
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace( ((1+x)/(1-x))^(1/4)*exp(x*(3 + x)/2) )) \\ G. C. Greubel, May 16 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( ((1+x)/(1-x))^(1/4)*Exp(x*(3+x)/2) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 16 2019
(Sage) m = 30; T = taylor(((1+x)/(1-x))^(1/4)*exp(x*(3+x)/2), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 16 2019
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
N. J. A. Sloane, Jan 16 2000
STATUS
approved