A340415
Number of sets of nonempty words with a total of n letters over octonary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
Original entry on oeis.org
1, 1, 3, 13, 60, 326, 2065, 14508, 116845, 676579, 4533285, 29337447, 204274255, 1401597565, 10464806200, 75242714351, 588938921227, 4060713617519, 30141138974325, 217182619165093, 1630762746458645, 11987353708674543, 91946531392941646, 683807822490949653
Offset: 0
-
b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
add(b(n-j, j, t-1)/j!, j=i..n/t))
end:
g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
end:
a:= n-> h(n$2, min(n, 8)):
seq(a(n), n=0..32);
A340416
Number of sets of nonempty words with a total of n letters over nonary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
Original entry on oeis.org
1, 1, 3, 13, 60, 326, 2065, 14508, 116845, 1039459, 6710565, 48872487, 350817295, 2619846205, 20019859960, 158415989711, 1300359929707, 10644485545679, 91963547963925, 715052566412773, 5842504427274965, 47435773495721103, 390005026265914606, 3225674439739003413
Offset: 0
-
b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
add(b(n-j, j, t-1)/j!, j=i..n/t))
end:
g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
end:
a:= n-> h(n$2, min(n, 9)):
seq(a(n), n=0..32);
A340417
Number of sets of nonempty words with a total of n letters over denary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
Original entry on oeis.org
1, 1, 3, 13, 60, 326, 2065, 14508, 116845, 1039459, 10339365, 72459687, 581246095, 4483235005, 36697945720, 298344453071, 2601248199787, 22469318990159, 208007606797845, 1867498245975013, 17978675539264085, 153181998023380623, 1392447676785436846
Offset: 0
-
b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
add(b(n-j, j, t-1)/j!, j=i..n/t))
end:
g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
end:
a:= n-> h(n$2, min(n, 10)):
seq(a(n), n=0..32);