A258495
Number of words of length 2n such that all letters of the octonary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting doublets into the initially empty word.
Original entry on oeis.org
1430, 143208, 8488440, 389948856, 15390120042, 549818906780, 18329867191350, 581350326663600, 17769492060922914, 528200606751594392, 15368894406877386408, 439845149792754810984, 12426477142114470011642, 347532158068343623121916, 9642227504194296532321086
Offset: 8
-
A:= proc(n, k) option remember; `if`(n=0, 1, k/n*
add(binomial(2*n, j)*(n-j)*(k-1)^j, j=0..n-1))
end:
T:= (n, k)-> add((-1)^i*A(n, k-i)/(i!*(k-i)!), i=0..k):
a:= n-> T(n, 8):
seq(a(n), n=8..25);
A258496
Number of words of length 2n such that all letters of the nonary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting doublets into the initially empty word.
Original entry on oeis.org
4862, 629850, 47432550, 2728352253, 133216751525, 5829093450180, 236006398327050, 9025008152896320, 330547676678287002, 11710509049983422030, 404211829411082901714, 13667296618312167097605, 454559414725395785663741, 14918526141220986683667840
Offset: 9
-
A:= proc(n, k) option remember; `if`(n=0, 1, k/n*
add(binomial(2*n, j)*(n-j)*(k-1)^j, j=0..n-1))
end:
T:= (n, k)-> add((-1)^i*A(n, k-i)/(i!*(k-i)!), i=0..k):
a:= n-> T(n, 9):
seq(a(n), n=9..25);
A258497
Number of words of length 2n such that all letters of the denary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting doublets into the initially empty word.
Original entry on oeis.org
16796, 2735810, 255290156, 17977098425, 1063758951255, 55927419074670, 2700837720153300, 122411464503168984, 5284666028132079380, 219622926821644989478, 8855064908059488718600, 348436223706779520860457, 13441577595226619289460295, 510180504585665885463323546
Offset: 10
-
A:= proc(n, k) option remember; `if`(n=0, 1, k/n*
add(binomial(2*n, j)*(n-j)*(k-1)^j, j=0..n-1))
end:
T:= (n, k)-> add((-1)^i*A(n, k-i)/(i!*(k-i)!), i=0..k):
a:= n-> T(n, 10):
seq(a(n), n=10..25);
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