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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

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: A218348 A320827 A077831 * A001835 A079935 A281593

Adjacent sequences:  A032949 A032950 A032951 * A032953 A032954 A032955

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 06 2002

STATUS

approved

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Last modified February 21 15:34 EST 2019. Contains 320374 sequences. (Running on oeis4.)