A317982 Expansion of 14*x*(29 + 784*x + 1974*x^2 + 784*x^3 + 29*x^4) / (1 - x)^7.

406, 13818, 115836, 545860, 1858290, 5124126, 12182968, 25945416, 50745870, 92745730, 160386996, 264896268, 420839146, 646725030, 965662320, 1406064016, 2002403718, 2796022026, 3835983340, 5179983060, 6895305186, 9059830318, 11763094056, 15107395800

Offset: 1

Author

Colin Barker, Aug 13 2018

Keywords

• nonn
• easy

Comments

Seems to be the second column of A316387.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A316387, A317981, A317983, A317984.

Programs

Mathematica

LinearRecurrence[{7,-21,35,-35,21,-7,1},{406,13818,115836,545860,1858290,5124126,12182968},30] (* Harvey P. Dale, Nov 15 2022 *)

PARI

Vec(14*x*(29 + 784*x + 1974*x^2 + 784*x^3 + 29*x^4) / (1 - x)^7 + O(x^40))

PARI

a(n) = 70*n^6 + 210*n^5 + 175*n^4 - 42*n^2 - 7*n

Formula

G.f.: 14*x*(29 + 784*x + 1974*x^2 + 784*x^3 + 29*x^4) / (1 - x)^7.

a(n) = 70*n^6 + 210*n^5 + 175*n^4 - 42*n^2 - 7*n.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.