A071748 - OEIS

A071748

Expansion of (1+x^4*C^2)*C^3, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

1, 3, 9, 28, 91, 302, 1021, 3507, 12209, 42991, 152866, 548148, 1979990, 7198055, 26316577, 96701545, 356941485, 1322891115, 4920919230, 18366138480, 68756266170, 258118218960, 971492416674, 3665120443878, 13857614540714

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OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..1665

FORMULA

(-6+4*n)*a(n) + (-6-13*n)*a(n+1) + (16+7*n)*a(n+2) + (-22-5*n)*a(n+3) + (32+5*n)*a(n+4) + (-8-n)*a(n+5) = 0. - Robert Israel, Jul 30 2018

MAPLE

f:= gfun:-rectoproc({(-6+4*n)*a(n)+(-6-13*n)*a(n+1)+(16+7*n)*a(n+2)+(-22-5*n)*a(n+3)+(32+5*n)*a(n+4)+(-8-n)*a(n+5), a(0) = 1, a(1) = 3, a(2) = 9, a(3) = 28, a(4) = 91, a(5) = 302, a(6) = 1021}, a(n), remember):

map(f, [$0..30]); # Robert Israel, Jul 30 2018

MATHEMATICA

Join[{1, 3}, RecurrenceTable[{(-13n-6) a[n+1] + (7n+16) a[n+2] + (-5n-22)* a[n+3] + (5n+32) a[n+4] + (-n-8) a[n+5] + (4n-6) a[n] == 0, a[2] == 9, a[3] == 28, a[4] == 91, a[5] == 302, a[6] == 1021}, a, {n, 2, 30}]] (* Jean-François Alcover, Aug 29 2022, after Robert Israel *)

PROG

(PARI) C = (1-(1-4*x)^(1/2))/(2*x); Vec((1+x^4*C^2)*C^3 + O(x^20)) \\ Felix Fröhlich, Jul 30 2018

CROSSREFS

Cf. A000108.

Sequence in context: A189940 A047047 A071744 * A071752 A071756 A176673

Adjacent sequences: A071745 A071746 A071747 * A071749 A071750 A071751

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 06 2002

STATUS

approved