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A014318 Convolution of Catalan numbers and powers of 2. 9
1, 3, 8, 21, 56, 154, 440, 1309, 4048, 12958, 42712, 144210, 496432, 1735764, 6145968, 21986781, 79331232, 288307254, 1054253208, 3875769606, 14315659632, 53097586284, 197677736208, 738415086066 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals triangle A106270 * A000079, the powers of 2. - Gary W. Adamson, Apr 02 2009

Binomial transform of A097332: (1, 2, 3, 5, 9, 18, 39,...). - Gary W. Adamson, Aug 01 2011

Hankel transform is A087960. - Wathek Chammam, Dec 02 2011

LINKS

Fung Lam, Table of n, a(n) for n = 0..1600

W. Chammam, F. Marcellán and R. Sfaxi, Orthogonal polynomials, Catalan numbers, and a general Hankel determinant evaluation, Linear Algebra Appl. (2011), in press

FORMULA

a(n) = Sum(2^(n-j) * binomial(2j,j)/(j+1), j=0..n). - Emeric Deutsch, Oct 16 2008

G.f.: (1-sqrt(1-4*z))/(2*z*(1-2*z)). - Emeric Deutsch, Oct 16 2008

Recurrence: (n+1)*a(n) = 32*(2*n-7)*a(n-5) + 48*(8-3*n)*a(n-4) + 8*(16*n-29)*a(n-3) + 4*(13-14*n)*a(n-2) + 12*n*a(n-1), n>=5. - Fung Lam, Mar 09 2014

Asymptotics: a(n) ~ 2^(2n+1)/n^(3/2)/sqrt(Pi). - Fung Lam, Mar 21 2014

MAPLE

a:=proc(n) options operator, arrow: sum(2^(n-j)*binomial(2*j, j)/(j+1), j=0..n) end proc: seq(a(n), n=0..23); # Emeric Deutsch, Oct 16 2008

CROSSREFS

Cf. A000108, A097332, A106270.

Sequence in context: A008909 A006835 * A158495 A273720 A018037 A018038

Adjacent sequences:  A014315 A014316 A014317 * A014319 A014320 A014321

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 20 15:22 EDT 2018. Contains 316388 sequences. (Running on oeis4.)