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A098618 Products of A007482 and Catalan numbers: a(n) = A007482(n)*A000108(n). 3
1, 3, 22, 195, 1946, 20790, 232716, 2693691, 31979090, 387243714, 4764470932, 59391201870, 748472730628, 9520446996300, 122067269204760, 1575965219205195, 20470515781159170, 267325017886787850 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Radius of convergence: r = (sqrt(17)-3)/16; A(r) = sqrt(2+6/sqrt(17)). Recurrence of A007482 is A007482(n) = 3*A007482(n-1) + 2*A007482(n-2). More generally, given {S} such that: S(n) = b*S(n-1) + c*S(n-2), |b|>0, |c|>0, then Sum_{n>=0} S(n)*Catalan(n)*x^n = sqrt( (1-2*b*x - sqrt(1-4*b*x-16*c*x^2))/(2*b^2+8*c) )/x.

LINKS

Table of n, a(n) for n=0..17.

FORMULA

G.f.: A(x) = sqrt((1-6*x - sqrt(1-12*x-32*x^2))/34 )/x.

n*(n+1)*a(n) -6*n*(2*n-1)*a(n-1) -8*(2*n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Nov 17 2018

EXAMPLE

Begins: {1*1, 3*1, 11*2, 39*5, 139*14, 495*42, 1763*132, 6279*429,...}.

PROG

(PARI) {a(n)=binomial(2*n, n)/(n+1)*((3+sqrt(17))^(n+1)-(3-sqrt(17))^(n+1))/2^(n+1)/sqrt(17)}

CROSSREFS

Cf. A007482, A000108, A098614, A098616, A098619.

Sequence in context: A046743 A121952 A250888 * A207326 A006783 A330668

Adjacent sequences:  A098615 A098616 A098617 * A098619 A098620 A098621

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 09 2004

STATUS

approved

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Last modified May 16 19:46 EDT 2021. Contains 343951 sequences. (Running on oeis4.)