A113632 a(n) = 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6 + 8*n^7 + 9*n^8 + 10*n^9.

1, 55, 9217, 280483, 3378745, 23803711, 118513705, 462945547, 1512003793, 4303999495, 10987654321, 25678050355, 55776799177, 113924725903, 220792014745, 408951042331, 728121033505, 1252121211607, 2087920281313

Offset: 0

Author

Jonathan Vos Post, Jan 14 2006

Keywords

• easy
• nonn
• changed

Comments

1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 8*x^7 + 9*x^8 + 10*x^9 is the derivative of 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 = (x^11 - 1)/(x-1).

Examples

			a(5) = 1 + 2*5 + 3*5^2 + 4*5^3 + 5*5^4 + 6*5^5 + 7*5^6 + 8*5^7 + 9*5^8 + 10*5^9 = 23803711 is prime.
a(30) = 1 + 2*30 + 3*30^2 + 4*30^3 + 5*30^4 + 6*30^5 + 7*30^6 + 8*30^7 + 9*30^8 + 10*30^9 = 202915112960761 is prime.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A056578, A056579.

Programs

Mathematica

With[{eq=Total[Range[10](n^Range[0,9])]},Table[eq,{n,0,20}]] (* Harvey P. Dale, Mar 14 2011 *)

Formula

a(n) = 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6 + 8*n^7 + 9*n^8 + 10*n^9.

G.f.: (1+x*(45+x*(8712+x*(190668+x*(982290+x*(1543254+x*(784080+x*(116268+x*(3477+5*x)))))))))/(x-1)^10. - Harvey P. Dale, Mar 14 2011