The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A038629

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A038629

Convolution of Catalan numbers A000108 with Catalan numbers but C(0)=1 replaced by 3.
(history; published version)

#37 by R. J. Mathar at Wed Mar 29 07:44:07 EDT 2023

STATUS

editing

approved

#36 by R. J. Mathar at Wed Mar 29 07:44:03 EDT 2023

FORMULA

D-finite with recurrence (n+2)*a(n) -2*(n+1)*a(n-1) +4*(-2*n+3)*a(n-2)=0. - R. J. Mathar, Dec 10 2013

STATUS

approved

editing

#35 by Michael De Vlieger at Tue Feb 14 08:57:12 EST 2023

STATUS

reviewed

approved

#34 by Joerg Arndt at Tue Feb 14 02:12:56 EST 2023

STATUS

proposed

reviewed

#33 by Amiram Eldar at Tue Feb 14 01:39:29 EST 2023

STATUS

editing

proposed

#32 by Amiram Eldar at Tue Feb 14 01:36:17 EST 2023

DATA

3, 4, 9, 24, 70, 216, 693, 2288, 7722, 26520, 92378, 325584, 1158924, 4160240, 15043725, 54747360, 200360130, 736928280, 2722540590, 10098646800, 37594507860, 140415097680, 526024740930, 1976023374624, 7441754696100, 28091245875056, 106268257060308, 402815053582368

#31 by Amiram Eldar at Tue Feb 14 01:31:08 EST 2023

FORMULA

From Amiram Eldar, Feb 14 2023: (Start)

Sum_{n>=0} 1/a(n) = Pi/(9*sqrt(3)) + 5/9.

Sum_{n>=0} (-1)^n/a(n) = 17/75 - 22*log(phi)/(75*sqrt(5)), where phi is the golden ratio (A001622). (End)

STATUS

approved

editing

#30 by Charles R Greathouse IV at Thu Sep 08 08:44:53 EDT 2022

PROG

(MAGMAMagma) [6*Binomial(2*n, n)/(n+2): n in [0..30]]; // Vincenzo Librandi, May 10 2012

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#29 by Peter Luschny at Mon Mar 28 11:24:24 EDT 2022

STATUS

proposed

approved

#28 by Michel Marcus at Mon Mar 28 11:16:50 EDT 2022

STATUS

editing

proposed