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A190049

Expansion of (16+24*x+2*x^2)/(x-1)^6.
(history; published version)

#12 by Charles R Greathouse IV at Thu Sep 08 08:45:56 EDT 2022

PROG

(MAGMAMagma) [(21*n^5+245*n^4+1105*n^3+2395*n^2+2474*n+960)/60: n in [0..50]]; // Vincenzo Librandi, May 07 2011

Discussion

Thu Sep 08

08:45

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

#11 by Bruno Berselli at Thu Jan 11 03:11:16 EST 2018

STATUS

reviewed

approved

#10 by Michel Marcus at Thu Jan 11 02:43:17 EST 2018

STATUS

proposed

reviewed

#9 by G. C. Greubel at Thu Jan 11 02:28:50 EST 2018

STATUS

editing

proposed

#8 by G. C. Greubel at Thu Jan 11 02:27:58 EST 2018

NAME

Expansion of (16+24*x+2*x^2)/(x-1)^6.

LINKS

<a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

FORMULA

G.f.: (16 +24*x +2*x^2)/(x-1-x)^6.

a(n) = 16*binomial(n+5,5) +24*binomial(n+4,5) +2*binomial(n+3,5).

a(n) = A091894(5,0)*binomial(n+5,5) + A091894(5,1)*binomial(n+4,5) + A091894(5,2)*binomial(n+3,5).

a(n) = (21*n^5 +245*n^4 +1105*n^3 +2395*n^2 +2474*n +960)/60.

MATHEMATICA

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {16, 120, 482, 1412, 3402, 7168}, 30] (* or *) CoefficientList[Series[(16 +24*x +2*x^2)/(1-x)^6, {x, 0, 50}], x] (* G. C. Greubel, Jan 10 2018 *)

PROG

(MAGMA) [(21*n^5+245*n^4+1105*n^3+2395*n^2+2474*n+960)/60: n in [0..50]]; // _Vincenzo Librandi, _, May 07 2011

(PARI) x='x+O('x^30); Vec((16 +24*x +2*x^2)/(1-x)^6) \\ G. C. Greubel, Jan 10 2018

(PARI) for(n=0, 30, print1((21*n^5 +245*n^4 +1105*n^3 +2395*n^2 +2474*n +960)/60, ", ")) \\ G. C. Greubel, Jan 10 2018

STATUS

approved

editing

#7 by Russ Cox at Fri Mar 30 18:59:51 EDT 2012

AUTHOR

_Johannes W. Meijer (meijgia(AT)hotmail.com), _, May 06 2011

Discussion

Fri Mar 30

18:59

OEIS Server: https://oeis.org/edit/global/295

#6 by Joerg Arndt at Fri May 13 06:16:41 EDT 2011

STATUS

reviewed

approved

#5 by Joerg Arndt at Thu May 12 12:34:37 EDT 2011

STATUS

proposed

reviewed

#4 by Joerg Arndt at Thu May 12 12:34:29 EDT 2011

NAME

Expansion of GF(x) = (16+24*x+2*x^2)/(x-1)^6

FORMULA

GF(x) = G.f.: (16+24*x+2*x^2)/(x-1)^6

a(n) = A091894(5,0)*binomial(n+5,5) + A091894(5,1)*binomial(n+4,5) + A091894(5,2)*binomial(n+3,5)

#3 by Vincenzo Librandi at Sat May 07 01:35:19 EDT 2011

LINKS

Vincenzo Librandi, <a href="/A190049/b190049.txt">Table of n, a(n) for n = 0..1000</a>

PROG

(MAGMA) [(21*n^5+245*n^4+1105*n^3+2395*n^2+2474*n+960)/60: n in [0..50]]; // Vincenzo Librandi, May 07 2011