0,2

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

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).

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)

(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 *)

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

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

Cf. A008455, A017077.

Sequence in context: A384643 A290503 A172889 * A017171 A017387 A017507

Adjacent sequences: A017084 A017085 A017086 * A017088 A017089 A017090

nonn,easy

approved