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%I M4519 N1913 #33 Jul 08 2017 01:10:12
%S 1,8,36,148,554,2094,7624,27428,96231,332159,1126792,3769418,12437966,
%T 40544836,130643734,416494314,1314512589,4110009734,12737116845,
%U 39144344587,119350793207,361173596536,1085171968872
%N Euler transform of A000579.
%C In general, if g.f. = Product_{k>=1} 1/(1-x^k)^binomial(k+m-2,m-1) and m >= 1, then log(a(n)) ~ (m+1) * Zeta(m+1)^(1/(m+1)) * (n/m)^(m/(m+1)). - _Vaclav Kotesovec_, Mar 12 2015
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A000428/b000428.txt">Table of n, a(n) for n = 1..1000</a>
%H A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, <a href="http://dx.doi.org/10.1017/S0305004100042171">Some computations for m-dimensional partitions</a>, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100.
%H A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, <a href="/A000219/a000219.pdf">Some computations for m-dimensional partitions</a>, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100. [Annotated scanned copy]
%H Vaclav Kotesovec, <a href="/A000428/a000428.txt">Asymptotic formula</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%p with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d,j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: a:= etr(n-> binomial(n+5,6)): seq(a(n), n=1..30); # _Alois P. Heinz_, Sep 08 2008
%t nn = 30; b = Table[Binomial[n, 6], {n, 6, nn + 6}]; Rest[CoefficientList[Series[Product[1/(1 - x^m)^b[[m]], {m, nn}], {x, 0, nn}], x]] (* _T. D. Noe_, Jun 20 2012 *)
%o (PARI) a(n)=if(n<0, 0, polcoeff(exp(sum(k=1, n, x^k/(1-x^k)^7/k, x*O(x^n))), n)) /* _Joerg Arndt_, Apr 16 2010 */
%Y Cf. A000041, A000219, A000294, A000335, A000391, A000417, A255965.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
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