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%I #28 Jul 27 2021 04:04:42
%S 44,309,1214,3539,8544,18089,34754,61959,104084,166589,256134,380699,
%T 549704,774129,1066634,1441679,1915644,2506949,3236174,4126179,
%U 5202224,6492089,8026194,9837719,11962724,14440269,17312534,20624939,24426264
%N a(n) = (1/n!)*A001689(n).
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/enumfun.pdf">Enumerative Formulas for Some Functions on Finite Sets</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = n^5 + 10*n^4 + 45*n^3 + 100*n^2 + 109*n + 44.
%F 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), with a(0)=44, a(1)=309, a(2)=1214, a(3)=3539, a(4)=8544, a(5)=18089. - _Harvey P. Dale_, Jul 25 2012
%F G.f.: (x^5 + 10*x^3 + 20*x^2 + 45*x + 44) / (x-1)^6. - _Colin Barker_, Jun 15 2013
%F P-recursive: n*a(n) = (n+6)*a(n-1) - a(n-2) with a(0) = 44 and a(1) = 309. Cf. A094791 and A096307. - _Peter Bala_, Jul 25 2021
%t Table[n^5+10n^4+45n^3+100n^2+109n+44,{n,0,30}] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{44,309,1214,3539,8544,18089},30]
%o (PARI) a(n)=n^5+10*n^4+45*n^3+100*n^2+109*n+44 \\ _Charles R Greathouse IV_, Oct 16 2015
%Y Cf. A001563, A001564, A001565, A001688, A001689, A023043, A096307.
%Y Cf. A094791, A094792, A094793, A094795.
%K nonn,easy
%O 0,1
%A _Benoit Cloitre_, Jun 11 2004
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