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%I M4854 #64 Feb 18 2018 12:29:10
%S 1,12,90,520,2535,10908,42614,153960,521235,1669720,5098938,14931072,
%T 42124380,114945780,304351020,784087848,1970043621,4837060800,
%U 11626305640,27398234760,63388751544,144156086776,322590526350
%N Number of partitions of n into parts of 12 kinds.
%C Euler transform of A010851. - _Alois P. Heinz_, Oct 17 2008
%C Convolution square of A005758 = A006922: (1, 24, 324, 3200, 25650, ...). - _Gary W. Adamson_, Jun 13 2009
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Seiichi Manyama, <a href="/A005758/b005758.txt">Table of n, a(n) for n = 0..1000</a> (first 201 terms from T. D. Noe)
%H Roland Bacher, P. De La Harpe, <a href="https://hal.archives-ouvertes.fr/hal-01285685/document">Conjugacy growth series of some infinitely generated groups</a>. 2016, hal-01285685v2.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a>
%F G.f.: Product ( 1 - x^k )^(-12).
%F Expansion of q^(1/2) * eta(q)^-12 in powers of q. - _Michael Somos_, Mar 07 2012
%F Convolution inverse of A000735.
%F a(n) ~ exp(2 * Pi * sqrt(2*n)) / (2^(15/4) * n^(15/4)). - _Vaclav Kotesovec_, Feb 28 2015
%F a(0) = 1, a(n) = (12/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 26 2017
%F G.f.: exp(12*Sum_{k>=1} x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Feb 06 2018
%e G.f. = 1 + 12*x + 90*x^2 + 520*x^3 + 2535*x^4 + 10908*x^5 + 42614*x^6 + ...
%e G.f. = 1/q + 12*q + 90*q^3 + 520*q^5 + 2535*q^7 + 10908*q^9 + 42614*q^11 + ...
%p with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*12, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # _Alois P. Heinz_, Oct 17 2008
%t CoefficientList[Series[1/QPochhammer[x,x]^12,{x,0,30}],x] (* _Harvey P. Dale_, Apr 21 2011 *)
%o (PARI) {a(n) = if( n<0, 0, polcoeff( 1 / eta(x + x * O(x^n))^12, n))}; /* _Michael Somos_, Mar 07 2012 */
%Y 12th column of A144064. - _Alois P. Heinz_, Oct 17 2008
%Y Cf. A006922. - _Gary W. Adamson_, Jun 13 2009
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_, _Simon Plouffe_
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