A293586 Number of compositions of n where each part i is marked with a word of length i over a nonary alphabet whose letters appear in alphabetical order and all nine letters occur at least once in the composition.

7087261, 492006708, 19423259316, 574637640288, 14193955791576, 309660911167464, 6171397007611848, 114853532449557600, 2026594842428425320, 34277110454602760762, 560261324259420037164, 8904738970375872782112, 138290600270036591006520, 2106511986693346884064584

Offset: 9

Author

Alois P. Heinz, Oct 12 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..885

Crossrefs

Column k=9 of A261781.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1,
      add(b(n-j, k)*binomial(j+k-1, k-1), j=1..n))
    end:
a:= n-> (k->add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k))(9):
seq(a(n), n=9..30);

Formula

a(n) = 90*a(n-1) - 3720*a(n-2) + 94140*a(n-3) - 1642368*a(n-4) + 21111972*a(n-5) - 208936444*a(n-6) + 1643906838*a(n-7) - 10544413816*a(n-8) + 56273496182*a(n-9) - 254124223400*a(n - 10) + 984813733064*a(n - 11) - 3313818868728*a(n - 12) + 9777617820932*a(n - 13) - 25505157099056*a(n - 14) + 59222241227144*a(n - 15) - 123105458091224*a(n - 16) + 230174411303404*a(n - 17) - 388610578141384*a(n - 18) + 594331344450528*a(n - 19) - 825476563250976*a(n - 20) + 1043293124084592*a(n - 21) - 1201650502768408*a(n - 22) + 1262594519234968*a(n - 23) - 1210928179506120*a(n - 24) + 1060266691901408*a(n - 25) - 847323181595664*a(n - 26) + 617639581793392*a(n - 27) - 410205458302944*a(n - 28) + 247843724510640*a(n - 29) - 135949707500048*a(n - 30) + 67526545242016*a(n - 31) - 30273460576096*a(n - 32) + 12201462236512*a(n - 33) - 4399521714368*a(n - 34) + 1410734015840*a(n - 35) - 399326676032*a(n - 36) + 98870585152*a(n - 37) - 21165129088*a(n - 38) + 3859085248*a(n - 39) - 587513600*a(n - 40) + 72658304*a(n - 41) - 7011968*a(n - 42) + 495360*a(n - 43) - 22784*a(n - 44) + 512*a(n - 45). - Vaclav Kotesovec, Oct 14 2017