A317981 Expansion of x*(125 + 8028*x + 42237*x^2 + 42272*x^3 + 8007*x^4 + 132*x^5 - x^6) / (1 - x)^8.

125, 9028, 110961, 684176, 2871325, 9402660, 25872833, 62572096, 136972701, 276971300, 524988145, 943023888, 1618774781, 2672907076, 4267591425, 6616398080, 9995653693, 14757360516, 21343778801, 30303773200, 42311023965, 58184203748, 78909220801

Offset: 1

Author

Colin Barker, Aug 13 2018

Keywords

• nonn
• easy

Comments

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

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A316387, A317982, A317983, A317984.

Programs

Mathematica

LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{125,9028,110961,684176,2871325,9402660,25872833,62572096},30] (* Harvey P. Dale, Dec 29 2024 *)

PARI

Vec(x*(125 + 8028*x + 42237*x^2 + 42272*x^3 + 8007*x^4 + 132*x^5 - x^6) / (1 - x)^8 + O(x^40))

PARI

a(n) = 20*n^7 + 70*n^6 + 70*n^5 - 28*n^3 - 7*n^2

Formula

G.f.: x*(125 + 8028*x + 42237*x^2 + 42272*x^3 + 8007*x^4 + 132*x^5 - x^6) / (1 - x)^8.

a(n) = 20*n^7 + 70*n^6 + 70*n^5 - 28*n^3 - 7*n^2.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.