A056579 1+2n+3n^2+4n^3+5n^4.

1, 15, 129, 547, 1593, 3711, 7465, 13539, 22737, 35983, 54321, 78915, 111049, 152127, 203673, 267331, 344865, 438159, 549217, 680163, 833241, 1010815, 1215369, 1449507, 1715953, 2017551, 2357265, 2738179, 3163497, 3636543

Offset: 0

Author

Henry Bottomley, Jun 29 2000

Keywords

• easy
• nonn

Examples

			For n>5 this is 54321 translated from base n to base 10
		

Links

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

Crossrefs

Note: 1+2x+3x^2+4x^3+5x^4 is derivative of 1+x+x^2+x^3+x^4 +x^5, i.e. A053700. Cf. A000012, A005408, A056109, A056578.

Programs

Mathematica

Join[{1},Table[Total[Table[i n^(i-1),{i,5}]],{n,30}]] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,15,129,547,1593},30] (* Harvey P. Dale, Sep 20 2017 *)

PARI

a(n)=1+2*n+3*n^2+4*n^3+5*n^4 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) =(A053700(n+1)-A053700(n-1))/2-10n^2-4n-2.

G.f.: -(3*x^4+42*x^3+64*x^2+10*x+1) / (x-1)^5. - Colin Barker, May 04 2013