OFFSET
-1,4
LINKS
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = stirling2(n+2,n)-(n+2)*stirling2(n+1,n)+((n+1)*(n+2))/2.
a(n-1) = Sum_{j=0..n} (j-1)^(n+2)*(-1)^(n-j)*binomial(n,j)/n!.
G.f.: -(6*x^2-4*x+1) / (x*(x-1)^5). - Colin Barker, Sep 06 2013
a(n) = Sum_{k=1..n+2} Sum_{i=1..k} (n-i+1)*(n-k+1). - Wesley Ivan Hurt, Sep 12 2017
MATHEMATICA
Table[n^4/8 + (5*n^3)/12 - n^2/8 - (5*n)/12 + 1, {n, -1, 50}] (* T. D. Noe, Jun 14 2013 *)
PROG
(PARI) x='x+O('x^99); Vec(-(6*x^2-4*x+1)/(x*(x-1)^5)) \\ Altug Alkan, Sep 13 2017
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Vladimir Kruchinin, Jun 13 2013
STATUS
approved