cp's OEIS Frontend

A294012 Number of multisets of exactly ten nonempty words with a total of n letters over n-ary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

%I A294012 #4 Oct 21 2017 21:31:32
%S A294012 1,2,7,22,73,240,818,2824,10004,36252,134594,512620,2002740,8037362,
%T A294012 33121048,140282194,610324801,2728518748,12524236605,59013698416,
%U A294012 285164364993,1412336246688,7161455061084,37150204129624,196943561689961,1066098326520738
%N A294012 Number of multisets of exactly ten nonempty words with a total of n letters over n-ary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
%H A294012 Alois P. Heinz, <a href="/A294012/b294012.txt">Table of n, a(n) for n = 10..809</a>
%F A294012 a(n) = [x^n y^10] Product_{j>=1} 1/(1-y*x^j)^A000085(j).
%p A294012 g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
%p A294012 b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n,
%p A294012       add(binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 11)
%p A294012     end:
%p A294012 a:= n-> coeff(b(n$2), x, 10):
%p A294012 seq(a(n), n=10..40);
%Y A294012 Column k=10 of A293808.
%Y A294012 Cf. A000085.
%K A294012 nonn
%O A294012 10,2
%A A294012 _Alois P. Heinz_, Oct 21 2017