|
| |
|
|
A064087
|
|
Generalized Catalan numbers C(4; n).
|
|
5
| |
|
|
1, 1, 5, 41, 413, 4641, 55797, 702297, 9137549, 121909457, 1658755685, 22929591433, 321111942781, 4546112358529, 64958195967957, 935566629270201, 13567825195172973, 197957440018622769, 2903721563443327557
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| a(n+1)= Y_{n}(n+1)= Z_{n} in the Derrida et al. 1992 reference (see A064094) for alpha=4, beta =1 (or alpha=1, beta=4).
|
|
|
FORMULA
| G.f.: (1+4*x*c(4*x)/3)/(1+x/3) = 1/(1-x*c(4*x)) with c(x) g.f. of Catalan numbers A000108.
a(n)= sum((n-m)*binomial(n-1+m, m)*(4^m)/n, m=0..n-1) = ((-1/3)^n)*(1-4*sum(C(k)*(-12)^k, k=0..n-1)), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
a(n) = Sum{ k= 0...n, A059365(n, k)*4^(n-k) } . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 19 2004
|
|
|
PROG
| (PARI) a(n)=if(n<0, 0, polcoeff(serreverse((x-3*x^2)/(1+x)^2+O(x^(n+1))), n)) (from R. Stephan)
|
|
|
CROSSREFS
| A064063 (C(3, n)).
Sequence in context: A058475 A199684 A177506 * A081215 A140095 A083073
Adjacent sequences: A064084 A064085 A064086 * A064088 A064089 A064090
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Sep 13 2001
|
| |
|
|
