A022526 Nexus numbers (n+1)^10-n^10.

1, 1023, 58025, 989527, 8717049, 50700551, 222009073, 791266575, 2413042577, 6513215599, 15937424601, 35979939623, 75941127625, 151396163127, 287395735649, 522861237151, 916482272673, 1554473326175, 2560599031177, 4108933742199, 6439880978201, 9880041813223

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Column k=9 of A047969.

Cf. A008454 (n^10).

Cf. A008292, A022525, A022527.

Programs

Magma

[(n+1)^10-n^10: n in [0..20]]; // Vincenzo Librandi, Nov 22 2011

Maple

b:=10: a:=n->(n+1)^b-n^b: seq(a(n),n=0..18); # Muniru A Asiru, Feb 28 2018

Mathematica

Table[(n+1)^10-n^10,{n,0,20}] (* Vincenzo Librandi, Nov 22 2011 *)

PARI

for(n=0,20, print1((n+1)^10 - n^10, ", ")) \\ G. C. Greubel, Feb 27 2018

Formula

G.f.: (x +1)*(x^8 +1012*x^7 +46828*x^6 +408364*x^5 +901990*x^4 +408364*x^3 +46828*x^2 +1012*x +1) / (x -1)^10. - Colin Barker, Dec 22 2012

a(n) = A008454(n+1) - A008454(n). - Michel Marcus, Feb 28 2018

G.f.: polylog(-10, x)*(1-x)/x. See the g.f. of Colin Barker (with expanded numerator), and the g.f. of the rows of A008292 by Vladeta Jovovic, Sep 02 2002. - Wolfdieter Lang, May 10 2021

Extensions

More terms from Colin Barker, Dec 22 2012