OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
From Bruno Berselli, Aug 05 2011: (Start)
G.f.: (33 + 62*x + 48*x^2 - 30*x^3 + 7*x^4)/(1-x)^6.
a(n) = (n+1)*(n^4 + 10*n^3 + 35*n^2 + 51*n + 33).
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). (End)
E.g.f.: (33 + 227*x + 313*x^2 + 136*x^3 + 21*x^4 + x^5)*exp(x). - Stefano Spezia, Nov 02 2018
EXAMPLE
For n=1, a(1) = 1 + 2^4 + 3^5 = 1 + 16 + 243 = 260.
MAPLE
seq(k^3+(k+1)^4+(k+2)^5, k=0..30); # Muniru A Asiru, Nov 02 2018
MATHEMATICA
#[[1]]^3+#[[2]]^4+#[[3]]^5&/@Partition[Range[0, 30], 3, 1] (* Harvey P. Dale, Jul 23 2012 *)
Table[(n+1)*(n^4 +10*n^3 +35*n^2 +51*n +33), {n, 0, 30}] (* G. C. Greubel, Nov 02 2018 *)
CoefficientList[Series[E^x (33 + 227 x + 313 x^2 + 136 x^3 + 21 x^4 + x^5), {x, 0, 50}], x]*Table[k!, {k, 0, 50}] (* Stefano Spezia, Nov 02 2018 *)
PROG
(Magma) [n^3+(n+1)^4+(n+2)^5: n in [0..30]]; // Vincenzo Librandi, Aug 05 2011
(PARI) vector(30, n, n--; (n+1)*(n^4 +10*n^3 +35*n^2 +51*n +33)) \\ G. C. Greubel, Nov 02 2018
(GAP) List([0..30], k->k^3+(k+1)^4+(k+2)^5); # Muniru A Asiru, Nov 02 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, May 31 2001
EXTENSIONS
Offset changed from 1 to 0 by Vincenzo Librandi, Aug 05 2011
STATUS
approved