A209263 a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5.

1, 15, 257, 1639, 6369, 18551, 44785, 94767, 181889, 323839, 543201, 868055, 1332577, 1977639, 2851409, 4009951, 5517825, 7448687, 9885889, 12923079, 16664801, 21227095, 26738097, 33338639, 41182849, 50438751, 61288865, 73930807, 88577889, 105459719

Offset

0,2

Comments

This is to 5 as A209262 1 + 2*n^2 + 3*n^3 + 4*n^4 is to 4. The subsequence of primes begins: 257, 181889, 7448687, 16664801, a(60) = 3940495201.

Links

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

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

G.f. ( 1+9*x+182*x^2+302*x^3+105*x^4+x^5 ) / (x-1)^6 . - R. J. Mathar, Jan 17 2013

Example

a(2) = 1 + 2*2^2 + 3*2^3 + 4*2^4 + 5*2^5 = 257.

Mathematica

With[{c=1+Total[Table[k n^k, {k, 2, 5}]]}, Table[c, {n, 0, 30}]] (* Harvey P. Dale, Aug 01 2016 *)

Prog

(Maxima) makelist(1 + 2*n^2 + 3*n^3 + 4*n^4 +5*n^5, n, 0, 20); /* Martin Ettl, Jan 15 2013*/
(PARI) a(n)=1+2*n^2+3*n^3+4*n^4+5*n^5 \\ Charles R Greathouse IV, Oct 16 2015
(Magma) [1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5: n in [0..30]]; // G. C. Greubel, Jan 04 2018

Crossrefs

Cf. A209262.

Sequence in context: A334995 A099273 A206230 * A180832 A361185 A013381

Adjacent sequences: A209260 A209261 A209262 * A209264 A209265 A209266

Keyword

nonn,easy

Author

Jonathan Vos Post, Jan 14 2013

Status

approved