|
| |
|
|
A032952
|
|
Expansion of (1+x*C^4)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
|
|
1
|
|
|
|
1, 3, 11, 41, 152, 561, 2067, 7618, 28118, 104006, 385662, 1433797, 5344510, 19973085, 74827395, 281000430, 1057628550, 3989213610, 15077120010, 57092280570, 216579650664, 822991216746, 3132339521966, 11939881979076, 45577753704252, 174218415470092, 666795041653916
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
|
|
|
FORMULA
|
Recurrence: (n+5)*(19*n-8)*a(n) = (113*n^2+307*n-76)*a(n-1) - 2*(2*n-1)*(37*n+36)*a(n-2). - Vaclav Kotesovec, Oct 08 2012
|
|
|
MATHEMATICA
|
Table[SeriesCoefficient[(1+x*((1-(1-4*x)^(1/2))/(2*x))^4)*((1-(1-4*x)^(1/2))/(2*x))^2, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 08 2012 *)
|
|
|
PROG
|
(PARI) x='x+O('x^66); C=(1-(1-4*x)^(1/2))/(2*x); Vec( (1+x*C^4)*C^2 ) \\ Joerg Arndt, May 04 2013
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
