OFFSET
1,1
COMMENTS
Row 2 of the convolution array A213833. - Clark Kimberling, Jul 04 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = n*(2*n^2 + 5*n - 1)/2. - Jon E. Schoenfield, Jun 24 2010
G.f.: x*(3+5*x-2*x^2)/(1-x)^4. - Vincenzo Librandi, Jul 06 2012
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jul 06 2012
E.g.f.: x*(6 + 11*x + 2*x^2)*exp(x)/2. - G. C. Greubel, Mar 01 2021
MAPLE
MATHEMATICA
CoefficientList[Series[(3+5*x-2*x^2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 06 2012 *)
PROG
(Magma) I:=[3, 17, 48, 102]; [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, Jul 06 2012
(Sage) [n*(2*n^2 +5*n -1)/2 for n in (1..40)] # G. C. Greubel, Mar 01 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 21 2009, Jun 29 2009
STATUS
approved