A317983 Expansion of 420*x*(1 + x)*(1 + 10*x + x^2) / (1 - x)^6.

420, 7140, 41160, 148680, 411180, 955500, 1963920, 3684240, 6439860, 10639860, 16789080, 25498200, 37493820, 53628540, 74891040, 102416160, 137494980, 181584900, 236319720, 303519720, 385201740, 483589260, 601122480, 740468400, 904530900, 1096460820

Offset: 1

Author

Colin Barker, Aug 13 2018

Keywords

• nonn
• easy

Comments

Seems to be the negative of the third column of A316387.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A000538, A316387, A317981, A317982, A317984.

Programs

PARI

Vec(420*x*(1 + x)*(1 + 10*x + x^2) / (1 - x)^6 + O(x^40))

PARI

a(n) = 84*n^5 + 210*n^4 + 140*n^3 - 14*n

Formula

G.f.: 420*x*(1 + x)*(1 + 10*x + x^2) / (1 - x)^6.

a(n) = 420 * A000538(n).

a(n) = 84*n^5 + 210*n^4 + 140*n^3 - 14*n.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.