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A293584 Number of compositions of n where each part i is marked with a word of length i over a septenary alphabet whose letters appear in alphabetical order and all seven letters occur at least once in the composition. 2
47293, 2075948, 53476920, 1058754564, 17866313444, 270907452704, 3807403790792, 50592275219138, 644225577441572, 7936529529027736, 95254972055989564, 1119634204276346052, 12939870424457764200, 147501747088827091436, 1662420626477581539972 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 7..975

FORMULA

a(n) = 56*a(n-1) - 1400*a(n-2) + 20804*a(n-3) - 206864*a(n-4) + 1472576*a(n-5) - 7857468*a(n-6) + 32533654*a(n-7) - 107414264*a(n-8) + 288967984*a(n-9) - 644267912*a(n - 10) + 1206205784*a(n - 11) - 1915352424*a(n - 12) + 2598569764*a(n - 13) - 3027512680*a(n - 14) + 3038439672*a(n - 15) - 2630187744*a(n - 16) + 1962871608*a(n - 17) - 1260043528*a(n - 18) + 692851920*a(n - 19) - 324225312*a(n - 20) + 127932656*a(n - 21) - 42016752*a(n - 22) + 11279872*a(n - 23) - 2411968*a(n - 24) + 395168*a(n - 25) - 46592*a(n - 26) + 3520*a(n - 27) - 128*a(n - 28). - 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))(7):

seq(a(n), n=7..30);

CROSSREFS

Column k=7 of A261781.

Sequence in context: A257723 A320621 A218097 * A263067 A234708 A069370

Adjacent sequences: A293581 A293582 A293583 * A293585 A293586 A293587

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 12 2017

STATUS

approved

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Last modified December 1 21:09 EST 2022. Contains 358484 sequences. (Running on oeis4.)