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.

1, 2, 7, 22, 73, 240, 818, 2824, 10004, 36252, 134594, 512620, 2002740, 8037362, 33121048, 140282194, 610324801, 2728518748, 12524236605, 59013698416, 285164364993, 1412336246688, 7161455061084, 37150204129624, 196943561689961, 1066098326520738

Offset

10,2

Links

Alois P. Heinz, Table of n, a(n) for n = 10..809

Formula

a(n) = [x^n y^10] Product_{j>=1} 1/(1-y*x^j)^A000085(j).

Maple

g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n,
      add(binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 11)
    end:
a:= n-> coeff(b(n$2), x, 10):
seq(a(n), n=10..40);

Crossrefs

Column k=10 of A293808.

Cf. A000085.

Sequence in context: A294009 A294010 A294011 * A293809 A307976 A114495

Adjacent sequences: A294009 A294010 A294011 * A294013 A294014 A294015

Keyword

nonn

Author

Alois P. Heinz, Oct 21 2017

Status

approved