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Number of triangular partitions of n of order 9.
1

%I #7 Sep 08 2022 08:46:17

%S 1,9,45,173,567,1654,4422,11040,26051,58638,126778,264670,535806,

%T 1055480,2028884,3814688,7029559,12717703,22622719,39618458,68384638,

%U 116456100,195837008,325462408,534921468,870044724,1401226327,2235733481,3535790660

%N Number of triangular partitions of n of order 9.

%H L. Carlitz, R. Scoville, <a href="http://dx.doi.org/10.1090/S0025-5718-1975-0366803-0">A generating function for triangular partitions</a>, Math. Comp. 29 (1975) 67-77.

%F G.f.: 1/((1-x)^9*(1-x^3)^8*(1-x^5)^7*(1-x^7)^6*(1-x^9)^5*(1-x^11)^4*(1-x^13)^3*(1-x^15)^2*(1-x^17)).

%t CoefficientList[Series[1/((1-x)^9 (1-x^3)^8 (1-x^5)^7 (1-x^7)^6 (1-x^9)^5 (1-x^11)^4 (1-x^13)^3 (1-x^15)^2 (1-x^17)), {x, 0, 50}], x]

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^9*(1-x^3)^8*(1-x^5)^7*(1-x^7)^6*(1-x^9)^5*(1-x^11)^4*(1-x^13)^3*(1-x^15)^2*(1-x^17))));

%Y Cf. similar sequences listed in A276235.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Sep 01 2016