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Number of triangular partitions of n of order 8.
1

%I #18 Oct 09 2024 04:36:11

%S 1,8,36,127,386,1050,2632,6187,13789,29396,60336,119818,231140,434555,

%T 798320,1436294,2535511,4398876,7510668,12635844,20969143,34357138,

%U 55625853,89060282,141101197,221350031,344008194,529925620,809497788,1226738457

%N Number of triangular partitions of n of order 8.

%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)^8*(1-x^3)^7*(1-x^5)^6*(1-x^7)^5*(1-x^9)^4*(1-x^11)^3*(1-x^13)^2*(1-x^15)).

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

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^8*(1-x^3)^7*(1-x^5)^6*(1-x^7)^5*(1-x^9)^4*(1-x^11)^3*(1-x^13)^2*(1-x^15)))); // Corrected by _Georg Fischer_, May 19 2019

%Y Cf. similar sequences listed in A276235.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Sep 01 2016

%E Terms a(10) onward corrected by _Georg Fischer_, May 19 2019