A209267 1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6 + 7*n^7 + 8*n^8.

1, 36, 3585, 73810, 669921, 3784176, 15721201, 52683870, 150652545, 381367036, 876543201, 1862778666, 3709924705, 6996023880, 12592235601, 21771494326, 36344967681, 58830704340, 92659184065, 142420804866, 214160664801, 315726318496

Offset

0,2

Comments

The n for which a(n) is prime begin: n = 174, 414, 474, 516, 546, 594, 714, 756, 804, 1386, 1596, 1734, 1806, 1986, 2514. - Joerg Arndt, Jan 15 2013

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

G.f.: (6*x^8 +1371*x^7 +27991*x^6 +115317*x^5 +131793*x^4 +42757*x^3 +3297*x^2 +27*x +1) / (1-x)^9. - Colin Barker, Jan 26 2013

Example

a(2) = 1 + 2*2^2 + 3*2^3 + 4*2^4 + 5*2^5 + 6*2^6 + 7*2^7 + 8*2^8 = 3585.

Mathematica

Table[Total[Table[i*n^i, {i, 2, 8}]]+1, {n, 0, 30}] (* Harvey P. Dale, Jan 26 2013 *)

Prog

(Maxima) makelist(1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6 + 7*n^7 + 8*n^8, n, 0, 20); /* Martin Ettl, Jan 15 2013 */
(PARI) for(n=0, 30, print1(1 + sum(k=2, 8, k*n^k), ", ")) \\ G. C. Greubel, Jan 05 2018
(Magma) [1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6 + 7*n^7 + 8*n^8: n in [0..30]]; // G. C. Greubel, Jan 05 2018

Crossrefs

Cf. A209262, A209263, A209264, A209265.

Sequence in context: A291911 A072377 A364175 * A120349 A120359 A194611

Adjacent sequences: A209264 A209265 A209266 * A209268 A209269 A209270

Keyword

nonn,easy

Author

Jonathan Vos Post, Jan 15 2013

Status

approved