A161006 Convolution of A000108 (Catalan numbers) with A126120 (Catalan numbers interpolated with 0's).

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

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: A000932 A187124 A369530 * 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