A090391 a(n) = n*(n^4 + 30*n^3 + 395*n^2 + 2910*n + 11064)/120.

0, 120, 312, 606, 1040, 1661, 2526, 3703, 5272, 7326, 9972, 13332, 17544, 22763, 29162, 36933, 46288, 57460, 70704, 86298, 104544, 125769, 150326, 178595, 210984, 247930, 289900, 337392, 390936, 451095, 518466, 593681, 677408

Offset: 0

Author

Philippe Deléham, Jan 31 2004

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A084938 (sixth diagonal), A090238.

Programs

Mathematica

Table[n (n^4 + 30 n^3 + 395 n^2 + 2910 n + 11064)/120, {n, 0, 40}] (* Bruno Berselli, Feb 12 2015 *)

PARI

concat(0, Vec(x*(71*x^4-316*x^3+534*x^2-408*x+120)/(x-1)^6 + O(x^100))) \\ Colin Barker, Feb 12 2015

PARI

vector(40, n, n--; n*(n^4+30*n^3+395*n^2+2910*n+11064)/120) \\ Bruno Berselli, Feb 12 2015

Formula

a(n) = A084938(n+5, n) = Sum_{k=0..5} A090238(5, k)*binomial(n, k).

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>5. - Colin Barker, Feb 12 2015

G.f.: x*(71*x^4-316*x^3+534*x^2-408*x+120) / (x-1)^6. - Colin Barker, Feb 12 2015

Extensions

Name rewritten by Bruno Berselli, Feb 12 2015