The On-Line Encyclopedia of Integer Sequences (OEIS)

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A191501

Expansion of 2-sqrt(1-4*x-4*x^2-4*x^3)
(history; published version)

#12 by N. J. A. Sloane at Thu Jan 30 21:29:16 EST 2020

FORMULA

D-finite with recurrence: n*a(n) +2*(-2*n+3)*a(n-1) +4*(-n+3)*a(n-2) +2*(-2*n+9)*a(n-3)=0. - R. J. Mathar, Jan 25 2020

Discussion

Thu Jan 30

21:29

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

#11 by R. J. Mathar at Sat Jan 25 09:31:02 EST 2020

STATUS

editing

approved

#10 by R. J. Mathar at Sat Jan 25 09:30:59 EST 2020

FORMULA

D-finite: n*a(n) +2*(-2*n+3)*a(n-1) +4*(-n+3)*a(n-2) +2*(-2*n+9)*a(n-3)=0. - R. J. Mathar, Jan 25 2020

STATUS

approved

editing

#9 by Russ Cox at Sat Mar 31 10:23:14 EDT 2012

AUTHOR

_Vladimir Kruchinin (kru(AT)ie.tusur.ru), _, Jun 03 2011

Discussion

Sat Mar 31

10:23

OEIS Server: https://oeis.org/edit/global/362

#8 by Joerg Arndt at Wed Jun 15 08:15:56 EDT 2011

STATUS

proposed

approved

#7 by Vladimir Kruchinin at Wed Jun 15 06:00:13 EDT 2011

NAME

Expansion of 2-sqrt(1-4*x-4*x^2-4*x^3)

STATUS

approved

proposed

#6 by Joerg Arndt at Wed Jun 08 10:37:56 EDT 2011

STATUS

reviewed

approved

#5 by Joerg Arndt at Wed Jun 08 09:07:19 EDT 2011

STATUS

proposed

reviewed

#4 by Joerg Arndt at Wed Jun 08 09:07:13 EDT 2011

FORMULA

a(n)=2*sum(k=1..n, (binomial(2*k-2,k-1) * sum(j=0..k, binomial(j,n-3*k+2*j) * binomial(k,j) ) )/k ), n>0, a(0)=1.

#3 by Joerg Arndt at Wed Jun 08 09:06:10 EDT 2011

FORMULA

a(n):=2*sum(k=1..n, (binomial(2*k-2,k-1)*sum(j=0..k, binomial(j,n-3*k+2*j)*binomial(k,j)))/k), n>0, a(0)=1.