OFFSET
0,3
COMMENTS
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
O.g.f.: x*(1 + x)*(1 + 3*x)/(1 - x)^6 = ((1 + 3*x)/(1 - x)^3)*(x*(1 + x)/(1 - x)^3).
a(n) = binomial(n+2, 3)*(4*n^2 + 3*n + 3)/10 = n*(n + 1)*(n + 2)*(4*n^2 + 3*n + 3)/60.
a(n) = Sum_{k=0..n} A071238(k).
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) for n>5. - Colin Barker, Oct 21 2016
MATHEMATICA
Table[n (n + 1) (n + 2) (4 n^2 + 3 n + 3)/60, {n, 0, 40}] (* Bruno Berselli, Oct 21 2016 *)
PROG
(PARI) concat(0, Vec(x*((1+x)*(1+3*x))/(1-x)^6 + O(x^50))) \\ Colin Barker, Oct 21 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 20 2016
STATUS
approved