The On-Line Encyclopedia of Integer Sequences (OEIS)

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A270784

Expansion of (1-sqrt(1-4*x^4/(1-x)^4))/(2*x^4*(1-x)).
(history; published version)

#32 by N. J. A. Sloane at Thu Jan 30 21:29:17 EST 2020

FORMULA

D-finite with recurrence: (n+4)*a(n) +(-6*n-19)*a(n-1) +5*(3*n+7)*a(n-2) +10*(-2*n-3)*a(n-3) +(11*n+18)*a(n-4) +(2*n-11)*a(n-5) +3*(-n+1)*a(n-6)=0. - R. J. Mathar, Jun 07 2016

Discussion

Thu Jan 30

21:29

OEIS Server: https://oeis.org/edit/global/2847

#31 by R. J. Mathar at Sat Jan 25 08:47:41 EST 2020

STATUS

editing

approved

#30 by R. J. Mathar at Sat Jan 25 08:47:38 EST 2020

FORMULA

ConjectureD-finite: (n+4)*a(n) +(-6*n-19)*a(n-1) +5*(3*n+7)*a(n-2) +10*(-2*n-3)*a(n-3) +(11*n+18)*a(n-4) +(2*n-11)*a(n-5) +3*(-n+1)*a(n-6)=0. - R. J. Mathar, Jun 07 2016

STATUS

approved

editing

#29 by N. J. A. Sloane at Mon Jun 05 19:06:39 EDT 2017

STATUS

proposed

approved

#28 by G. C. Greubel at Mon Jun 05 18:40:31 EDT 2017

STATUS

editing

proposed

#27 by G. C. Greubel at Mon Jun 05 18:40:16 EDT 2017

LINKS

G. C. Greubel, <a href="/A270784/b270784.txt">Table of n, a(n) for n = 0..1000</a>

STATUS

approved

editing

#26 by R. J. Mathar at Tue Jun 07 12:25:02 EDT 2016

STATUS

editing

approved

#25 by R. J. Mathar at Tue Jun 07 12:21:39 EDT 2016

FORMULA

Conjecture: (n+4)*a(n) +(-6*n-19)*a(n-1) +5*(3*n+7)*a(n-2) +10*(-2*n-3)*a(n-3) +(11*n+18)*a(n-4) +(2*n-11)*a(n-5) +3*(-n+1)*a(n-6)=0. - R. J. Mathar, Jun 07 2016

STATUS

approved

editing

#24 by Bruno Berselli at Fri Mar 25 08:57:34 EDT 2016

STATUS

editing

approved

#23 by Bruno Berselli at Fri Mar 25 08:57:22 EDT 2016

FORMULA

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

a(n) = ((n+4)/4) * Sum_{k=0..(n+4)/4} (binomial(2*k,k)*binomial(n+3,n-4*k)/(k+1)^2).

PROG

(Maxima) a(n):=((n+4)/4*sum((binomial(2*k, k)*binomial(n+3, n-4*k))/(k+1)^2, k, 0, (n+4)/4));

a(n):=((n+4)/4*sum((binomial(2*k, k)*binomial(n+3, n-4*k))/(k+1)^2, k, 0, (n+4)/4));

STATUS

proposed

editing