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URL: https://oeis.org/A152031

⇱ A152031 - OEIS

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A152031
a(n) = n^5 + n^4 + n^3 + n^2 + n.
4
0, 5, 62, 363, 1364, 3905, 9330, 19607, 37448, 66429, 111110, 177155, 271452, 402233, 579194, 813615, 1118480, 1508597, 2000718, 2613659, 3368420, 4288305, 5399042, 6728903, 8308824, 10172525, 12356630, 14900787, 17847788, 21243689, 25137930, 29583455
OFFSET
0,2
FORMULA
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) n>5, a(0)=0, a(1)=5, a(2)=62, a(3)=363, a(4)=1364, a(5)=3905. [Yosu Yurramendi, Sep 03 2013]
From Indranil Ghosh, Apr 05 2017: (Start)
G.f.: x*(5 + 32x + 66x^2 + 16x^3 + x^4)/(x - 1)^6.
E.g.f.: exp(x)*x*(5 + 26x + 32x^2 + 11x^3 + x^4).
(End)
a(n) = n*A053699(n). - Michel Marcus, Apr 05 2017
MAPLE
a:= n-> `if`(n=1, 5, (n^6-n)/(n-1)):
seq(a(n), n=0..35); # Alois P. Heinz, Aug 20 2013
MATHEMATICA
lst={}; Do[AppendTo[lst, n^5+n^4+n^3+n^2+n], {n, 0, 5!}]; lst
(* Other programs: *)
Table[Total[n^Range@ 5], {n, 0, 31}] (* or *)
CoefficientList[Series[x (5 + 32 x + 66 x^2 + 16 x^3 + x^4)/(x - 1)^6, {x, 0, 31}], x] (* Michael De Vlieger, Apr 05 2017 *)
PROG
(R)
a <- c(0, 5, 62, 363, 1364, 3905)
for(n in (length(a)+1):40) 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]
a
[Yosu Yurramendi, Sep 03 2013]
(PARI) a(n) = n^5 + n^4 + n^3 + n^2 + n; \\ Joerg Arndt, Sep 03 2013
(Python) def a(n): return n**5 + n**4 + n**2 + n # Indranil Ghosh, Apr 05 2017
CROSSREFS
Column k=5 of A228275.
Cf. A053699.
Sequence in context: A116163 A394654 A092823 * A302181 A357350 A360345
KEYWORD
nonn
AUTHOR
STATUS
approved