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A293744 Number of sets of nonempty words with a total of n letters over quinary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter. 5
1, 1, 2, 6, 15, 45, 135, 422, 1357, 4503, 15301, 53225, 189070, 684540, 2522194, 9441960, 35867225, 138080428, 538155330, 2121211604, 8448577175, 33974559322, 137842934746, 563885092371, 2324435490519, 9650120731330, 40329864236526, 169593208033062 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: Product_{j>=1} (1+x^j)^A049401(j).

MAPLE

g:= proc(n) option remember;

      `if`(n<3, [1, 1, 2][n+1], ((3*n^2+17*n+15)*g(n-1)

       +(n-1)*(13*n+9)*g(n-2) -15*(n-1)*(n-2)*g(n-3)) /

       ((n+4)*(n+6)))

    end:

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(b(n-i*j, i-1)*binomial(g(i), j), j=0..n/i)))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..35);

MATHEMATICA

g[n_] := g[n] = If[n<3, {1, 1, 2}[[n+1]], ((3*n^2 + 17*n + 15)*g[n-1] + (n-1)*(13*n + 9)*g[n-2] - 15*(n-1)*(n-2)*g[n-3]) / ((n+4)*(n+6))];

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, i - 1]* Binomial[g[i], j], {j, 0, n/i}]]];

a[n_] := b[n, n];

Table[a[n], {n, 0, 35}] (* Jean-Fran├žois Alcover, Jun 06 2018, from Maple *)

CROSSREFS

Column k=5 of A293112.

Cf. A049401, A293735.

Sequence in context: A052870 A293743 A001444 * A293745 A293746 A293747

Adjacent sequences:  A293741 A293742 A293743 * A293745 A293746 A293747

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 15 2017

STATUS

approved

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Last modified May 13 16:56 EDT 2021. Contains 343862 sequences. (Running on oeis4.)