A017087 a(n) = (8*n + 1)^11.

1, 31381059609, 34271896307633, 2384185791015625, 50542106513726817, 550329031716248441, 3909821048582988049, 20635899893042801193, 87507831740087890625, 313726685568359708377, 984770902183611232881

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Composition of A008455(n) and A017077(n). - Wesley Ivan Hurt, Jul 17 2025

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Crossrefs

Cf. A008455, A017077.

Programs

Magma

[(8*n+1)^11: n in [0..20]]; // Vincenzo Librandi, Jul 11 2011

Mathematica

(8*Range[0,10]+1)^11 (* or *) LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{1,31381059609,34271896307633,2384185791015625,50542106513726817,550329031716248441,3909821048582988049,20635899893042801193,87507831740087890625,313726685568359708377,984770902183611232881,2775173073766990340489},20] (* Harvey P. Dale, Sep 08 2017 *)
CoefficientList[Series[(1 + 31381059597*x + 33895323592391*x^2 + 1974994185258003*x^3 + 24186918344729610*x^4 + 93655732195384290*x^5 + 134070558743608110*x^6 + 73557591075608934*x^7 + 14545208676272997*x^8 + 849143191166465*x^9 + 8626027938459*x^10 + 1977326743*x^11)/(-1 + x)^12, {x, 0, 15}], x] (* Wesley Ivan Hurt, Jul 17 2025 *)

PARI

a(n)=(8*n+1)^11 \\ Charles R Greathouse IV, Aug 11 2014

Formula

From Wesley Ivan Hurt, Jul 17 2025: (Start)

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).

G.f.: (1 + 31381059597*x + 33895323592391*x^2 + 1974994185258003*x^3 +24186918344729610*x^4 + 93655732195384290*x^5 + 134070558743608110*x^6 + 73557591075608934*x^7 + 14545208676272997*x^8 + 849143191166465*x^9 + 8626027938459*x^10 + 1977326743*x^11)/(-1 + x)^12.

a(n) = A008455(A017077(n)). (End)