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A145127 a(n) = 1 + (144 + (50 + (35 + (10 + n)*n)*n)*n)*n/120.

%I A145127 #12 Sep 08 2022 08:45:38
%S A145127 1,3,9,25,61,132,259,470,801,1297,2013,3015,4381,6202,8583,11644,
%T A145127 15521,20367,26353,33669,42525,53152,65803,80754,98305,118781,142533,
%U A145127 169939,201405,237366,278287,324664,377025,435931,501977,575793,658045,749436
%N A145127 a(n) = 1 + (144 + (50 + (35 + (10 + n)*n)*n)*n)*n/120.
%C A145127 (1 + 3x + 9x^2 + ...) = (1 + 3x + 6x^2 + 10x^3 + ...) * (1 + 3x^2 + 6x^3 + 10x^4 + ...). - _Gary W. Adamson_, Jul 27 2010
%H A145127 Vincenzo Librandi, <a href="/A145127/b145127.txt">Table of n, a(n) for n = 0..1000</a>
%F A145127 G.f.: (x^4 - 4*x^3 + 6*x^2 - 3*x + 1) / (1-x)^6.
%p A145127 a := n-> 1+ (144+ (50+ (35+ (10+ n) *n) *n) *n) *n/120: seq (a(n), n=0..40);
%o A145127 (Magma) [1 + (144 + (50 + (35 + (10 + n)*n)*n)*n)*n/120: n in [0..40]]; // _Vincenzo Librandi_, May 19 2011
%Y A145127 6th row of A145153. See row 6 of A145140/A145141 for rational coefficients and A145142 for 120 * coefficients of polynomial.
%K A145127 nonn
%O A145127 0,2
%A A145127 _Alois P. Heinz_, Oct 03 2008