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A161006 Convolution of A000108 (Catalan numbers) with A126120 (Catalan numbers interpolated with 0's). 1
1, 1, 3, 6, 18, 49, 155, 486, 1614, 5414, 18630, 64828, 228740, 814485, 2926323, 10588486, 38561814, 141214570, 519711666, 1921126036, 7129756188, 26555090618, 99228108222, 371886366620, 1397548389644, 5265130603468 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

FORMULA

G.f.: C(x)C(x^2), where C(x) = (1-sqrt(1-4x))/(2x) is the Catalan function. - Emeric Deutsch, Jun 22 2009

Conjecture: -(47*n-42)*(n+3)*(n+2)*(n+1)*a(n) + 2*(n+2)*(n+1)*(270*n^2 - 523*n + 126)*a(n-1) - 8*(n+1)*(211*n^3 - 1022*n^2 + 946*n + 63)*a(n-2) + 8*(-212*n^4 - 326*n^3 + 2489*n^2 - 1636*n + 126)*a(n-3) + 16*(985*n^4 - 8154*n^3 + 23771*n^2 - 28164*n + 11151)*a(n-4) + 32*(-386*n^4 + 5771*n^3 - 29314*n^2 + 60721*n - 43533)*a(n-5) - 64*(n-4)*(2*n-9)*(258*n^2 - 1193*n + 1267)*a(n-6) + 128*(n-5)*(2*n-9)*(2*n-11)*(82*n-203)*a(n-7) = 0. - R. J. Mathar, Oct 04 2014

MAPLE

C := x-> (1/2-(1/2)*sqrt(1-4*x))/x: G := C(x)*C(x^2): Gser := series(G, x = 0, 30): seq(coeff(Gser, x, n), n = 0 .. 27); # Emeric Deutsch, Jun 22 2009

CROSSREFS

Cf. A000108, A126120.

Sequence in context: A019308 A000932 A187124 * A148560 A148561 A123891

Adjacent sequences:  A161003 A161004 A161005 * A161007 A161008 A161009

KEYWORD

nonn

AUTHOR

Philippe Deléham, Jun 02 2009

EXTENSIONS

Extended by Emeric Deutsch, Jun 22 2009

STATUS

approved

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Last modified July 14 15:26 EDT 2020. Contains 335729 sequences. (Running on oeis4.)