OFFSET
1,1
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = n*(n+1)*(n+2)*(n+7)*(n^2+13*n+46)/48.
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-3,3), for n >= 3. - Milan Janjic, Dec 20 2008
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7), with a(1)=60, a(2)=342, a(3)=1175, a(4)=3135, a(5)=7140, a(6)=14560, a(7)=27342. - Harvey P. Dale, Oct 31 2011
G.f.: x*(8*x^3-41*x^2+78*x-60) / (x-1)^7. - Colin Barker, Aug 15 2014
a(n) = A000292(n) * (n+7)*(n^2+13*n+46)/8. - R. J. Mathar, Oct 01 2016
MAPLE
seq(n*(n+1)*(n+2)*(n+7)*(n^2+13*n+46)/48, n=1..40); # Muniru A Asiru, May 19 2018
MATHEMATICA
Table[n(n+1)(n+2)(n+7)(n^2+13n+46)/48, {n, 30}] (* or *) LinearRecurrence[ {7, -21, 35, -35, 21, -7, 1}, {60, 342, 1175, 3135, 7140, 14560, 27342}, 30] (* Harvey P. Dale, Oct 31 2011 *)
PROG
(PARI) Vec(x*(8*x^3-41*x^2+78*x-60)/(x-1)^7 + O(x^100)) \\ Colin Barker, Aug 15 2014
(Magma) [n*(n+1)*(n+2)*(n+7)*(n^2+13*n+46)/48: n in [1..40]]; // Vincenzo Librandi, May 03 2018
(GAP) List([1..30], n->n*(n+1)*(n+2)*(n+7)*(n^2+13*n+46)/48); # Muniru A Asiru, May 19 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved