A209264 a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4 +5*n^5 + 6*n^6.

1, 21, 641, 6013, 30945, 112301, 324721, 800661, 1754753, 3512485, 6543201, 11497421, 19248481, 30938493, 48028625, 72353701, 106181121, 152274101, 213959233, 295198365, 400664801, 535823821, 707017521, 921553973, 1187800705

Offset

0,2

Comments

This is to 6 as A209263 1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 is to 5, and to 5 as A209262 1 + 2*n^2 + 3*n^3 + 4*n^4 is to 4. The subsequence of primes begins: 641, 921553973.

Links

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

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: (5*x^6+238*x^5+1615*x^4+1932*x^3+515*x^2+14*x+1)/(1-x)^7. - Colin Barker, Jan 26 2013

Example

a(2) = 1 + 2*2^2 + 3*2^3 + 4*2^4 +5*2^5 + 6*2^6 = 641.

Mathematica

Table[Sum[k*n^k, {k, 2, 6}], {n, 0, 30}] (* G. C. Greubel, Jan 05 2018 *)

Prog

(Maxima) makelist(1 + 2*n^2 + 3*n^3 + 4*n^4 +5*n^5 + 6*n^6, n, 0, 20); /* Martin Ettl, Jan 25 2013 */
(PARI) for(n=0, 30, print1(1 + sum(k=2, 6, k*n^k), ", ")) \\ G. C. Greubel, Jan 04 2018
(Magma) [1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6: n in [0..30]]; // G. C. Greubel, Jan 04 2018

Crossrefs

Cf. A209262, A209263.

Sequence in context: A141265 A025752 A163032 * A012501 A027408 A177840

Adjacent sequences: A209261 A209262 A209263 * A209265 A209266 A209267

Keyword

nonn,easy

Author

Jonathan Vos Post, Jan 14 2013

Status

approved