A081912 a(n) = 6^n*(n^2 - n + 72)/72.

1, 6, 37, 234, 1512, 9936, 66096, 443232, 2985984, 20155392, 136048896, 917070336, 6167549952, 41358864384, 276451356672, 1841557856256, 12224809598976, 80871817347072, 533189772509184, 3503818505060352, 22952550207062016

Offset: 0

Author

Paul Barry, Mar 31 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081911 6th binomial transform of (1,0,1,0,0,0,...). Case k=6 where a(n,k) = k^n*(n^2 - n + 2k^2)/(2k^2) with g.f. (1 - 2kx + (k^2+1)x^2)/(1-kx)^3.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..150
• Index entries for linear recurrences with constant coefficients, signature (18,-108,216).

Programs

Magma

[6^n*(n^2-n+72)/72: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011

Formula

a(n) = 6^n*(n^2 - n + 72)/72.

G.f.: (1 - 12x + 37x^2)/(1-6x)^3.