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 A274254 Number of partitions of n^11 into at most three parts. 5

%I #14 Mar 17 2024 20:03:49

%S 1,1,350550,2615176875,1466017600854,198682173665365,

%T 10968475501587457,325818421703912376,6148914695531484502,

%U 82064241864324799212,833333333383333333334,6783562449045969261416,46005119909741205651457,267653239830467338960133

%N Number of partitions of n^11 into at most three parts.

%H Colin Barker, <a href="/A274254/b274254.txt">Table of n, a(n) for n = 0..1000</a>

%F Coefficient of x^(n^11) in 1/((1-x)*(1-x^2)*(1-x^3)).

%F G.f.: (1 -20*x +350738*x^2 +2607814224*x^3 +1411172155915*x^4 +168441916780374*x^5 +7099123683305188*x^6 +135099678234258306*x^7 +1347312342856212192*x^8 +7787883425074758928*x^9 +28110747299021064172*x^10 +67156060497799730456*x^11 +111034930795496260254*x^12 +130841757853019123380*x^13 +111034930795581623376*x^14 +67156060497892295980*x^15 +28110747298805651529*x^16 +7787883425149430772*x^17 +1347312342924772018*x^18 +135099678177816904*x^19 +7099123689451223*x^20 +168441921705222*x^21 +1411171249180*x^22 +2607681186*x^23 +348502*x^24) / ((1 -x)^23*(1 +x)*(1 +x +x^2)).

%F a(n) = A001399(n^11) = round((n^11+3)^2/12). - _Alois P. Heinz_, Jun 16 2016

%o (PARI)

%o \\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)).

%o b(n) = round(real((47+9*(-1)^n + 8*exp(-2/3*I*n*Pi) + 8*exp((2*I*n*Pi)/3) + 36*n+6*n^2)/72))

%o vector(50, n, n--; b(n^11))

%Y A subsequence of A001399.

%Y Cf. A274250 (n^2), A274251 (n^3), A274252 (n^5), A274253 (n^7).

%K nonn,easy

%O 0,3

%A _Colin Barker_, Jun 16 2016

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Last modified July 13 02:50 EDT 2024. Contains 374265 sequences. (Running on oeis4.)