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, 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

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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

a(n) ~ 13*2^(2*n+2)/(sqrt(Pi)*n^(3/2)). - 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

Sequence in context: A320827 A335793 A077831 * A001835 A079935 A281593

Adjacent sequences: A032949 A032950 A032951 * A032953 A032954 A032955

Keyword

nonn

Author

N. J. A. Sloane, Jun 06 2002

Status

approved