A316458 Expansion of 60*x*(1 + 4*x + x^2) / (1 - x)^5.

60, 540, 2160, 6000, 13500, 26460, 47040, 77760, 121500, 181500, 261360, 365040, 496860, 661500, 864000, 1109760, 1404540, 1754460, 2166000, 2646000, 3201660, 3840540, 4570560, 5400000, 6337500, 7392060, 8573040, 9890160, 11353500, 12973500, 14760960

Offset: 1

Author

Colin Barker, Aug 12 2018

Keywords

• nonn
• easy

Comments

Seems to be the negative of the second column of A316349.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A000537, A316349, A316457, A316459.

Programs

PARI

Vec(60*x*(1 + 4*x + x^2) / (1 - x)^5 + O(x^40))

PARI

a(n) = 15*n^4 + 30*n^3 + 15*n^2

Formula

G.f.: 60*x*(1 + 4*x + x^2) / (1 - x)^5.

a(n) = 60 * A000537(n).

a(n) = 15*n^4 + 30*n^3 + 15*n^2.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.