OFFSET
0,2
COMMENTS
N(4,n) where N(4,x) is the 4th Narayana polynomial.
a(n) + A016921(n+1) = (n+2)^3. [Bruno Berselli, Jun 24 2012]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = N(4,n) = Sum_{k>0} A001263(4, k)*n^(k-1) = (n+1)*(n^2+5*n+1).
G.f.: (1 + 10*x - 5*x^2) / (x-1)^4. - R. J. Mathar, Sep 07 2011
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 24 2012
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {1, 14, 45, 100}, 40] (* Vincenzo Librandi, Jun 24 2012 *)
PROG
(PARI) n^3+6*n^2+6*n+1 \\ Charles R Greathouse IV, Jan 17 2012
(Magma) I:=[1, 14, 45, 100]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 24 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Jan 22 2004
STATUS
approved