A052574 Expansion of e.g.f. (1-2x)/(1-3x+x^2).

1, 1, 4, 30, 312, 4080, 64080, 1174320, 24595200, 579519360, 15172012800, 436929292800, 13726748851200, 467182235520000, 17123385600921600, 672444082582272000, 28167703419727872000, 1253648083943743488000

Offset

0,3

Links

Table of n, a(n) for n=0..17.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 517

Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Formula

E.g.f.: -(-1+2*x)/(1-3*x+x^2).

Recurrence: {a(1)=1, a(0)=1, (n^2+3*n+2)*a(n)+(-6-3*n)*a(n+1)+a(n+2)=0}.

Sum((1/5)*(-1+4*_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^2-3*_Z+1))*n!.

a(n) = n!*Sum_{k=1..n} binomial(n-1,k-1)*Fibonacci(k); n>0. [Vladimir Kruchinin, Sep 01 2010]

a(n) = n!*A001519(n). - R. J. Mathar, Nov 27 2011

Maple

spec := [S, {S=Sequence(Prod(Z, Sequence(Prod(Z, Sequence(Z)))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Crossrefs

Sequence in context: A088794 A239841 A145348 * A158834 A139086 A243244

Adjacent sequences: A052571 A052572 A052573 * A052575 A052576 A052577

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Status

approved