A032952 - OEIS

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

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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