A017384 a(n) = (10*n + 9)^8.

43046721, 16983563041, 500246412961, 5352009260481, 33232930569601, 146830437604321, 513798374428641, 1517108809906561, 3936588805702081, 9227446944279201, 19925626416901921, 40213853471634241, 76686282021340161

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Crossrefs

Cf. A001016, A017377.

Programs

Magma

[(10*n+9)^8: n in [0..20]]; // Vincenzo Librandi, Sep 01 2011

Mathematica

(10 Range[0, 19] + 9)^8 (* Alonso del Arte, Dec 02 2017 *)

PARI

a(n) = (10*n + 9)^8 \\ Iain Fox, Dec 02 2017

Formula

From Iain Fox, Dec 02 2017: (Start)

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9), n > 8.

G.f.: (43046721 + 16596142552*x + 348944027548*x^2 + 1457583888744*x^3 + 1652522683270*x^4 + 520202222824*x^5 + 35893629468*x^6 + 214358872*x^7 + x^8)/(1-x)^9.

E.g.f.: exp(x)*(43046721 + 16940516320*x + 233161166800*x^2 + 650362944000*x^3 + 614936700000*x^4 + 243902400000*x^5 + 43988000000*x^6 + 3520000000*x^7 + 100000000*x^8). (End)

a(n) = A001016(A017377(n)). - Felix Fröhlich, Dec 03 2017