A016954 a(n) = (6n+3)^10.

59049, 3486784401, 576650390625, 16679880978201, 205891132094649, 1531578985264449, 8140406085191601, 34050628916015625, 119042423827613001, 362033331456891249, 984930291881790849, 2446194060654759801, 5631351470947265625, 12157665459056928801

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

Cf. A008454, A016762, A016945, A016946, A016947, A016948, A016949, A016950, A016951, A016952, A016953.

Subsequence of A008454.

Programs

Magma

[(6*n+3)^10: n in [0..20]]; // Vincenzo Librandi, May 06 2011

Maple

A016954:=n->(6*n+3)^10: seq(A016954(n), n=0..20); # Wesley Ivan Hurt, Aug 22 2016

Mathematica

(6 Range[0, 20] + 3)^10 (* Wesley Ivan Hurt, Aug 22 2016 *)

Formula

From Wesley Ivan Hurt, Aug 22 2016: (Start)

G.f.: 59049*(1 + 59038*x + 9116141*x^2 + 178300904*x^3 + 906923282*x^4 + 1527092468*x^5 + 906923282*x^6 + 178300904*x^7 + 9116141*x^8 + 59038*x^9 + x^10)/(1-x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>10.

a(n) = A008454(A016945(n)). (End)

From Amiram Eldar, Mar 30 2022: (Start)

a(n) = A016946(n)^5 = A016949(n)^2.

a(n) = 3^10*A016762(n).

Sum_{n>=0} 1/a(n) = 31*Pi^10/171421608960. (End)