A317984 Expansion of 140*x*(1 + 4*x + x^2) / (1 - x)^5.

140, 1260, 5040, 14000, 31500, 61740, 109760, 181440, 283500, 423500, 609840, 851760, 1159340, 1543500, 2016000, 2589440, 3277260, 4093740, 5054000, 6174000, 7470540, 8961260, 10664640, 12600000, 14787500, 17248140, 20003760, 23077040, 26491500, 30271500

Offset: 1

Author

Colin Barker, Aug 13 2018

Keywords

• nonn
• easy

Comments

Seems to be the fourth column of A316387.

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. A316387, A317981, A317982, A317983.

Programs

PARI

Vec(140*x*(1 + 4*x + x^2) / (1 - x)^5 + O(x^40))

PARI

a(n) = 35*n^4 + 70*n^3 + 35*n^2

Formula

G.f.: 140*x*(1 + 4*x + x^2) / (1 - x)^5.

a(n) = 35*n^4 + 70*n^3 + 35*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.