A168124 a(n) = n^2*(n^6+1)/2.

0, 1, 130, 3285, 32776, 195325, 839826, 2882425, 8388640, 21523401, 50000050, 107179501, 214990920, 407865445, 737894626, 1281445425, 2147483776, 3487878865, 5509980450, 8491781701, 12800000200, 18911429901, 27437937010, 39155492905, 55037657376

Offset: 0

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Subsequence of A027441 and A057590.

Programs

Magma

[n^2*(n^6+1)/2: n in [0..25]]; // Vincenzo Librandi, Jul 14 2016

Mathematica

Table[n^2*(n^6 + 1)/2, {n, 0, 50}] (* G. C. Greubel, Jul 13 2016 *)

Formula

O.g.f.: x*(1 + x)*(1 + 120*x + 2031*x^2 + 5776*x^3 + 2031*x^4 + 120*x^5 + x^6)/(1 - x)^9. - Bruno Berselli, Jul 14 2016

E.g.f.: x*(2 + 128*x + 966*x^2 + 1701*x^3 + 1050*x^4 + 266*x^5 + 28*x^6 + x^7)*exp(x)/2. - Bruno Berselli, Jul 14 2016

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). - Wesley Ivan Hurt, Jun 09 2023