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A293587
Number of compositions of n where each part i is marked with a word of length i over a denary alphabet whose letters appear in alphabetical order and all ten letters occur at least once in the composition.
2
102247563, 8624400680, 408962920820, 14395560938040, 419691762832900, 10733397639516016, 249286917950186760, 5378992003398157520, 109550762660946047540, 2130231901794898870880, 39890088439337327537706, 724087830188007677450600, 12806950694169650253597100
OFFSET
10,1
LINKS
FORMULA
a(n) = 110*a(n-1) - 5610*a(n-2) + 176880*a(n-3) - 3881988*a(n-4) + 63363036*a(n-5) - 803190784*a(n-6) + 8158333238*a(n-7) - 68032529026*a(n-8) + 474993355914*a(n-9) - 2822235496730*a(n - 10) + 14467586756760*a(n - 11) - 64737065451880*a(n - 12) + 255368816478596*a(n - 13) - 895592944790280*a(n - 14) + 2812645592347868*a(n - 15) - 7959012851067608*a(n - 16) + 20400177554223892*a(n - 17) - 47577190249945824*a(n - 18) + 101351234640525316*a(n - 19) - 197858458654518512*a(n - 20) + 354970398396888856*a(n - 21) - 586639546887371480*a(n - 22) + 894863479752319328*a(n - 23) - 1262018115661289704*a(n - 24) + 1647713711756348440*a(n - 25) - 1993736153901444400*a(n - 26) + 2237552288722011272*a(n - 27) - 2330463862262027344*a(n - 28) + 2253297285769248336*a(n - 29) - 2022772844930193632*a(n - 30) + 1685689150486091056*a(n - 31) - 1303653883506384160*a(n - 32) + 935094847660607024*a(n - 33) - 621597594038060528*a(n - 34) + 382531198553819968*a(n - 35) - 217648454420883104*a(n - 36) + 114307777283928640*a(n - 37) - 55307833610580384*a(n - 38) + 24597346495674400*a(n - 39) - 10027630547676256*a(n - 40) + 3735272463460864*a(n - 41) - 1266527133905728*a(n - 42) + 389159192308096*a(n - 43) - 107781232918912*a(n - 44) + 26735152254272*a(n - 45) - 5893548603520*a(n - 46) + 1143628773376*a(n - 47) - 193030560256*a(n - 48) + 27910311552*a(n - 49) - 3387984128*a(n - 50) + 335821568*a(n - 51) - 26104576*a(n - 52) + 1492480*a(n - 53) - 55808*a(n - 54) + 1024*a(n - 55). - Vaclav Kotesovec, Oct 14 2017
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))(10):
seq(a(n), n=10..30);
CROSSREFS
Column k=10 of A261781.
Sequence in context: A348810 A306502 A218091 * A263070 A116670 A073643
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 12 2017
STATUS
approved