The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A216541 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A216541

Product of Lucas and Catalan numbers: a(n) = A000032(n+1)*A000108(n).
(history; published version)

#14 by N. J. A. Sloane at Fri May 05 01:39:01 EDT 2023

STATUS

reviewed

approved

#13 by Joerg Arndt at Fri May 05 00:15:23 EDT 2023

STATUS

proposed

reviewed

#12 by Amiram Eldar at Fri May 05 00:12:33 EDT 2023

STATUS

editing

proposed

#11 by Amiram Eldar at Fri May 05 00:06:43 EDT 2023

DATA

1, 3, 8, 35, 154, 756, 3828, 20163, 108680, 598026, 3342404, 18929092, 108374252, 626264700, 3647936160, 21396522915, 126262239570, 749087596620, 4465444206300, 26733390275130, 160663411399920, 968937572793060, 5862111195487560, 35569106862459300, 216395609659221564

FORMULA

Sum_{n>=0} a(n)/8^n = 8 - 2*sqrt(10). - Amiram Eldar, May 05 2023

MATHEMATICA

a[n_] := LucasL[n+1] * CatalanNumber[n]; Array[a, 25, 0] (* Amiram Eldar, May 05 2023 *)

STATUS

approved

editing

#10 by R. J. Mathar at Tue Sep 11 12:01:38 EDT 2012

STATUS

editing

approved

#9 by R. J. Mathar at Tue Sep 11 12:01:29 EDT 2012

FORMULA

n*(n+1)*a(n) -2*n*(2n-1)*a(n-1) -4*(2*n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Sep 11 2012

STATUS

approved

editing

#8 by Paul D. Hanna at Sat Sep 08 22:13:25 EDT 2012

STATUS

editing

approved

#7 by Paul D. Hanna at Sat Sep 08 22:13:21 EDT 2012

FORMULA

G.f. satisfies: A(x) = (2+5*x) - (1+4*x)*A(x) + x*(5+2*x)*A(x)^2 - 4*x^2*A(x)^3 + x^3*A(x)^4.

STATUS

approved

editing

#6 by Paul D. Hanna at Sat Sep 08 10:40:20 EDT 2012

STATUS

editing

approved

#5 by Paul D. Hanna at Sat Sep 08 10:40:17 EDT 2012

PROG

(PARI) {a(n)=(2*fibonacci(n)+fibonacci(n+21))*binomial(2*n, n)/(n+1)}

STATUS

approved

editing