cp's OEIS Frontend

A293585 Number of compositions of n where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order and all eight letters occur at least once in the composition.

%I A293585 #6 Oct 14 2017 10:51:39
%S A293585 545835,30532384,984910128,24082101504,496274574936,9104663637024,
%T A293585 153620123190816,2434519831873920,36763980389367378,
%U A293585 534505149483841568,7538836344403305280,103747819539055788640,1399283448432865901624,18560930972118370361856
%N A293585 Number of compositions of n where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order and all eight letters occur at least once in the composition.
%H A293585 Alois P. Heinz, <a href="/A293585/b293585.txt">Table of n, a(n) for n = 8..925</a>
%F A293585 a(n) = 72*a(n-1) - 2352*a(n-2) + 46452*a(n-3) - 624540*a(n-4) + 6112176*a(n-5) - 45535444*a(n-6) + 266958678*a(n-7) - 1264269754*a(n-8) + 4940034192*a(n-9) - 16203617768*a(n - 10) + 45247660712*a(n - 11) - 108803821608*a(n - 12) + 227386203188*a(n - 13) - 416072786528*a(n - 14) + 670510739364*a(n - 15) - 955987452656*a(n - 16) + 1210032902216*a(n - 17) - 1363000899064*a(n - 18) + 1368396317120*a(n - 19) - 1225293972272*a(n - 20) + 978413136792*a(n - 21) - 696053259552*a(n - 22) + 440365848816*a(n - 23) - 247084003008*a(n - 24) + 122486489680*a(n - 25) - 53377923152*a(n - 26) + 20315614688*a(n - 27) - 6696256832*a(n - 28) + 1890687584*a(n - 29) - 450764768*a(n - 30) + 89006080*a(n - 31) - 14167936*a(n - 32) + 1747264*a(n - 33) - 156672*a(n - 34) + 9088*a(n - 35) - 256*a(n - 36). - _Vaclav Kotesovec_, Oct 14 2017
%p A293585 b:= proc(n, k) option remember; `if`(n=0, 1,
%p A293585       add(b(n-j, k)*binomial(j+k-1, k-1), j=1..n))
%p A293585     end:
%p A293585 a:= n-> (k->add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k))(8):
%p A293585 seq(a(n), n=8..30);
%Y A293585 Column k=8 of A261781.
%K A293585 nonn
%O A293585 8,1
%A A293585 _Alois P. Heinz_, Oct 12 2017