A263689 a(n) = (2*n^6 - 6*n^5 + 5*n^4 - n^2 + 12)/12.

1, 1, 2, 34, 277, 1301, 4426, 12202, 29009, 61777, 120826, 220826, 381877, 630709, 1002002, 1539826, 2299201, 3347777, 4767634, 6657202, 9133301, 12333301, 16417402, 21571034, 28007377, 35970001, 45735626, 57617002, 71965909, 89176277, 109687426, 133987426, 162616577, 196171009, 235306402, 280741826

Offset: 0

Author

Ilya Gutkovskiy, Nov 20 2015

Keywords

• nonn
• easy

Examples

			a(0) = 1,
a(1) = 0^5 + 1 = 1,
a(2) = 1^5 + 1 = 2,
a(3) = 2^5 + 2 = 34,
a(4) = 3^5 + 34 = 227,
a(5) = 4^5 + 227 = 1301, etc.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A000124, A000539, A000584, A056520, A154323.

Programs

Mathematica

Table[(1/12) (12 + (-1 + n)^2 n^2 (-1 + 2 (-1 + n) n)), {n, 0, 35}]

PARI

first(m)=vector(m,n,n--;(2*n^6 - 6*n^5 + 5*n^4 - n^2 + 12)/12) \\ Anders Hellström, Nov 20 2015

Formula

G.f.: (1 - 6*x + 16*x^2 + 6*x^3 + 81*x^4 + 20*x^5 + 2*x^6)/(1 - x)^7.

a(n + 1) = a(n) + n^5, a(0) = 1.

a(n + 1) - a(n) = A000584(n).

a(n + 1) = A000539(n) + 1.

Sum_{n>0} 1/(a(n + 1) - a(n)) = zeta(5) = 1.036927755...