A016823 a(n) = (4n+1)^11.

1, 48828125, 31381059609, 1792160394037, 34271896307633, 350277500542221, 2384185791015625, 12200509765705829, 50542106513726817, 177917621779460413, 550329031716248441, 1532278301220703125, 3909821048582988049, 9269035929372191597, 20635899893042801193

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Crossrefs

Cf. A001020, A013669, A016813.

Programs

Magma

[(4*n+1)^11 : n in [0..20]]; // Wesley Ivan Hurt, Oct 10 2014

Maple

A016823:=n->(4*n+1)^11: seq(A016823(n), n=0..20); # Wesley Ivan Hurt, Oct 10 2014

Mathematica

Table[(4 n + 1)^11, {n, 0, 20}] (* Wesley Ivan Hurt, Oct 10 2014 *)
CoefficientList[Series[(1 + 48828113 x + 30795122175 x^2 + 1418810334759 x^3 + 14826379326378 x^4 + 50417667664170 x^5 + 64020606756990 x^6 + 31088834650350 x^7 + 5356480404741 x^8 + 261595441397 x^9 + 1975200979 x^10 + 177147 x^11)/(x - 1)^12, {x, 0, 30}], x] (* Wesley Ivan Hurt, Oct 10 2014 *)

Formula

From Wesley Ivan Hurt, Oct 10 2014 : (Start)

G.f.: (1 + 48828113*x + 30795122175*x^2 + 1418810334759*x^3 + 14826379326378*x^4 + 50417667664170*x^5 + 64020606756990*x^6 + 31088834650350*x^7 + 5356480404741*x^8 + 261595441397*x^9 + 1975200979*x^10 + 177147*x^11) / (x - 1)^12.

Recurrence: a(n) = 12*a(n-1)-66*a(n-2)+220*a(n-3)-495*a(n-4)+792*a(n-5)-924*a(n-6)+792*a(n-7)-495*a(n-8)+220*a(n-9)-66*a(n-10)+12*a(n-11)-a(n-12).

a(n) = A016813(n)^11 = A001020(A016813(n)). (End)

Sum_{n>=0} 1/a(n) = 50521*Pi^11/29727129600 + 2047*zeta(11)/4096. - Amiram Eldar, Apr 21 2023