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%I #15 Sep 08 2022 08:46:17
%S 1,6,21,61,156,361,781,1599,3124,5876,10696,18917,32627,55027,90948,
%T 147604,235610,370395,574181,878616,1328343,1985833,2937727,4303249,
%U 6245316,8984932,12819913,18149148,25503623,35586130,49321916,67922649,92967170,126503102
%N Number of triangular partitions of n of order 6.
%H Vincenzo Librandi, <a href="/A276235/b276235.txt">Table of n, a(n) for n = 0..1000</a>
%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.
%H <a href="/index/Rec#order_91">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 25, -45, 85, -135, 198, -298, 442, -627, 856, -1156, 1560, -2048, 2614, -3322, 4201, -5209, 6349, -7697, 9268, -11004, 12899, -15023, 17404, -19943, 22592, -25456, 28539, -31676, 34828, -38103, 41461, -44737, 47875, -50957, 53980, -56736, 59150, -61376, 63385, -64954, 66068, -66888, 67385, -67385, 66888, -66068, 64954, -63385, 61376, -59150, 56736, -53980, 50957, -47875, 44737, -41461, 38103, -34828, 31676, -28539, 25456, -22592, 19943, -17404, 15023, -12899, 11004, -9268, 7697, -6349, 5209, -4201, 3322, -2614, 2048, -1560, 1156, -856, 627, -442, 298, -198, 135, -85, 45, -25, 15, -6, 1).
%F G.f.: 1/((1-x)^6*(1-x^3)^5*(1-x^5)^4*(1-x^7)^3*(1-x^9)^2* (1-x^11)).
%t CoefficientList[Series[1/((1 - x)^6 (1 - x^3)^5 (1 - x^5)^4 (1 - x^7)^3 (1 - x^9)^2 (1 - x^11)), {x, 0, 50}],x]
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^6*(1-x^3)^5*(1-x^5)^4*(1-x^7)^3*(1-x^9)^2*(1-x^11))));
%o (PARI) Vec(1/((1-x)^6*(1-x^3)^5*(1-x^5)^4*(1-x^7)^3*(1-x^9)^2*(1-x^11)) + O(x^30)) \\ _Felix Fröhlich_, Aug 29 2016
%Y Cf. number of triangular partitions of n of order k: A000012 (k=1), A001840 (k=2), A084439 (k=3). A084446 (k=4), A084447 (k=5), this sequence (k=6), A276236 (k=7), A276279 (k=8), A276280 (k=9).
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Aug 29 2016
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