A368047 a(n) = (-1)^n * n*(n + 1)*(2*n + (-1)^n * (4*n + 5) + 1) / 12.

0, 1, 9, 10, 50, 35, 147, 84, 324, 165, 605, 286, 1014, 455, 1575, 680, 2312, 969, 3249, 1330, 4410, 1771, 5819, 2300, 7500, 2925, 9477, 3654, 11774, 4495, 14415, 5456, 17424, 6545, 20825, 7770, 24642, 9139, 28899, 10660, 33620, 12341

Offset: 0

Author

Peter Luschny, Dec 09 2023

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1).

Crossrefs

Cf. A368045, A368046.

Programs

Mathematica

A368047[n_]:=n(n+1)(2n+(-1)^n(4n+5)+1)(-1)^n/12;Array[A368047,50,0] (* or *)
LinearRecurrence[{0,4,0,-6,0,4,0,-1},{0,1,9,10,50,35,147,84},50] (* Paolo Xausa, Dec 10 2023 *)

Formula

a(n) = Sum_{n=0..k} (-1)^(n-k) *A368045(n, k).

G.f.: x*(1 + 9*x + 6*x^2 + 14*x^3 + x^4 + x^5)/((1 - x)^4*(1 + x)^4). - Stefano Spezia, Dec 10 2023