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%I #9 Dec 26 2023 22:38:58
%S 1,19,140,660,2370,7062,18348,42900,92235,185185,351208,634712,
%T 1100580,1841100,2984520,4705464,7237461,10887855,16055380,23250700,
%U 33120230,46473570,64314900,87878700
%N Fifth column (m=4) of triangle A060102.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
%F a(n) = (2*n^2+10*n+7)*binomial(n+6, 6)/7.
%F G.f.: (1+10*x+5*x^2)/(1-x)^9.
%F 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
%t 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 *)
%Y Cf. A060102, A060103.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Apr 06 2001