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Revision History for A360026

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Showing entries 1-10 | older changes

A360026

a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n-3*k,k) * Catalan(k).
(history; published version)

#23 by R. J. Mathar at Wed Jan 25 08:25:34 EST 2023

STATUS

editing

approved

#22 by R. J. Mathar at Wed Jan 25 08:25:23 EST 2023

FORMULA

D-finite with recurrence +(n+4)*a(n) +2*(-n-3)*a(n-1) +(n+2)*a(n-2) +4*(n-2)*a(n-4) +2*(-2*n+5)*a(n-5)=0. - R. J. Mathar, Jan 25 2023

STATUS

approved

editing

#21 by Joerg Arndt at Mon Jan 23 08:32:27 EST 2023

STATUS

reviewed

approved

#20 by Michel Marcus at Mon Jan 23 08:01:33 EST 2023

STATUS

proposed

reviewed

#19 by Seiichi Manyama at Mon Jan 23 07:29:03 EST 2023

STATUS

editing

proposed

#18 by Seiichi Manyama at Mon Jan 23 06:53:08 EST 2023

LINKS

Seiichi Manyama, <a href="/A360026/b360026.txt">Table of n, a(n) for n = 0..1000</a>

#17 by Seiichi Manyama at Mon Jan 23 06:15:36 EST 2023

FORMULA

G.f.: 2 / ( 1-x - + sqrt((1-x)^2 + 4*x^4*(1-x)) ).

STATUS

approved

editing

#16 by Michael De Vlieger at Sun Jan 22 11:35:06 EST 2023

STATUS

proposed

approved

#15 by Seiichi Manyama at Sun Jan 22 09:32:46 EST 2023

STATUS

editing

proposed

#14 by Seiichi Manyama at Sun Jan 22 09:28:53 EST 2023

FORMULA

G.f.: ( -2 / ( 1-x) + - sqrt((1-x)^2 + 4*x^4*(1-x)) ) / (2*x^4*(1-x)).

PROG

(PARI) my(N=50, x='x+O('x^(N+4))); Vec((-2/(1-x)+sqrt((1-x)^2+4*x^4*(1-x)))/(2*x^4*(1-x)))