A209262 a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4.

1, 10, 97, 424, 1249, 2926, 5905, 10732, 18049, 28594, 43201, 62800, 88417, 121174, 162289, 213076, 274945, 349402, 438049, 542584, 664801, 806590, 969937, 1156924, 1369729, 1610626, 1881985, 2186272, 2526049, 2903974, 3322801, 3785380

Offset

0,2

Comments

The subsequence of primes begins: 97, 1249, 18049, 43201, 162289, 438049, 2526049, a(32) = 4294657, a(44) = 15251809, a(48) = 21570049.

Links

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

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

G.f.: (4*x^4+29*x^3+57*x^2+5*x+1) / (1-x)^5. - Colin Barker, Jan 26 2013

Example

a(4) = 1 + 2*4^2 + 3*4^3 + 4*4^4 = 1249.

Mathematica

Table[Sum[k*n^k, {k, 2, 4}], {n, 0, 30}] (* G. C. Greubel, Jan 05 2018 *)

Prog

(Maxima) makelist(1 + 2*n^2 + 3*n^3 + 4*n^4, n, 0, 20); /* Martin Ettl, Jan 15 2013 */
(PARI) a(n)=1+2*n^2+3*n^3+4*n^4 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [1 + 2*n^2 + 3*n^3 + 4*n^4: n in [0..30]]; // G. C. Greubel, Jan 04 2018

Crossrefs

Sequence in context: A190986 A287831 A288430 * A308523 A190985 A044642

Adjacent sequences: A209259 A209260 A209261 * A209263 A209264 A209265

Keyword

nonn,easy

Author

Jonathan Vos Post, Jan 14 2013

Status

approved