A293970
Number of sets of exactly eight 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.
Original entry on oeis.org
10, 206, 1926, 13957, 85610, 476631, 2477550, 12289388, 58942808, 276126959, 1272626168, 5803545269, 26305047510, 118947441994, 538263144030, 2444159610896, 11163194878438, 51392032544011, 238939873029462, 1123916805738119, 5357138152220234, 25913264903132961
Offset: 21
-
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, 1, `if`(i<1, 0,
add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 9)
end:
a:= n-> coeff(b(n$2), x, 8):
seq(a(n), n=21..45);
A293971
Number of sets of exactly nine 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.
Original entry on oeis.org
45, 740, 7265, 54844, 355786, 2086218, 11402599, 59244154, 296592681, 1444795518, 6898985716, 32478508414, 151439118998, 702039301562, 3246061184641, 15011635714770, 69604533115983, 324297338323040, 1521325113273431, 7199243859471728, 34426802099939524
Offset: 25
-
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, 1, `if`(i<1, 0,
add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 10)
end:
a:= n-> coeff(b(n$2), x, 9):
seq(a(n), n=25..49);
A293972
Number of sets 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.
Original entry on oeis.org
120, 2010, 21082, 169846, 1173098, 7286181, 41993502, 228997683, 1198101638, 6074435686, 30073235682, 146248264684, 701957684114, 3338454463793, 15784582285468, 74407037119692, 350575594435412, 1654700449779204, 7840223330719670, 37363522942015498
Offset: 29
-
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, 1, `if`(i<1, 0,
add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 11)
end:
a:= n-> coeff(b(n$2), x, 10):
seq(a(n), n=29..53);