OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = binomial(n+4, n-1) + binomial(n, n-1).
a(n) = C(n+4, 5) + n = A000389(n+4) + n.
a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6), with a(1)=2, a(2)=8, a(3)=24, a(4)=60, a(5)=131, a(6)=258. - Harvey P. Dale, Apr 07 2013
G.f.: x*(x^4-4*x^3+6*x^2-4*x+2) / (x-1)^6. - Colin Barker, Mar 19 2015
E.g.f.: x*(240 + 240*x + 120*x^2 + 20*x^3 + x^4)*exp(x)/120. - G. C. Greubel, Nov 25 2017
MATHEMATICA
Table[Binomial[n+4, n-1]+Binomial[n, n-1], {n, 40}] (* or *) LinearRecurrence[ {6, -15, 20, -15, 6, -1}, {2, 8, 24, 60, 131, 258}, 40] (* Harvey P. Dale, Apr 07 2013 *)
PROG
(PARI) Vec(x*(x^4-4*x^3+6*x^2-4*x+2)/(x-1)^6 + O(x^100)) \\ Colin Barker, Mar 19 2015
(Magma) [n*(n^4 + 10*n^3 + 35*n^2 + 50*n + 144)/120: n in [1..30]]; // G. C. Greubel, Nov 25 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 07 1999
STATUS
approved