A060104 Fifth column (m=4) of triangle A060102.

1, 19, 140, 660, 2370, 7062, 18348, 42900, 92235, 185185, 351208, 634712, 1100580, 1841100, 2984520, 4705464, 7237461, 10887855, 16055380, 23250700, 33120230, 46473570, 64314900, 87878700

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Formula

a(n) = (2*n^2+10*n+7)*binomial(n+6, 6)/7.

G.f.: (1+10*x+5*x^2)/(1-x)^9.

a(0)=1, a(1)=19, a(2)=140, a(3)=660, a(4)=2370, a(5)=7062, a(6)=18348, a(7)=42900, a(8)=92235, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)- 126*a(n-4)+ 126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Nov 08 2012

Mathematica

Table[(2n^2+10n+7) Binomial[n+6, 6]/7, {n, 0, 30}] (* or *) LinearRecurrence[ {9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 19, 140, 660, 2370, 7062, 18348, 42900, 92235}, 30] (* Harvey P. Dale, Nov 08 2012 *)

Crossrefs

Cf. A060102, A060103.

Sequence in context: A235146 A057636 A104046 * A201151 A221600 A110694

Adjacent sequences: A060101 A060102 A060103 * A060105 A060106 A060107

Keyword

nonn,easy

Author

Wolfdieter Lang, Apr 06 2001

Status

approved