OFFSET
1,1
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = n*(n+1)*(3*n^2 + 35*n + 106)/24.
If we define f(n,i,a) = Sum_{k=0..n-i} binomial(n,k) * Stirling1(n-k,i) * Product_{j=0..k-1} (-a-j), then a(n-2) = f(n,n-2,3), for n >= 3. - Milan Janjic, Dec 20 2008
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Colin Barker, Aug 15 2014
G.f.: -x*(4*x^2-13*x+12) / (x-1)^5. - Colin Barker, Aug 15 2014
MAPLE
seq(n*(n+1)*(3*n^2+35*n+106)/24, n=1..40); # Muniru A Asiru, May 19 2018
MATHEMATICA
f[k_] := k + 2; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 30}] (* A024183 *)
(* Clark Kimberling, Dec 31 2011 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {12, 47, 119, 245, 445}, 40] (* Vincenzo Librandi, May 03 2018 *)
PROG
(PARI) Vec(-x*(4*x^2-13*x+12)/(x-1)^5 + O(x^100)) \\ Colin Barker, Aug 15 2014
(Magma) [n*(n+1)*(3*n^2+35*n+106)/24: n in [1..40]]; // Vincenzo Librandi, May 03 2018
(GAP) List([1..40], n->n*(n+1)*(3*n^2+35*n+106)/24); # Muniru A Asiru, May 19 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved