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 A320265 Number of proper multisets of nonempty words with a total of n letters over n-ary alphabet such that if a letter occurs in the multiset all predecessors occur at least once. 2
 1, 3, 23, 178, 1786, 20927, 282520, 4299263, 72750927, 1353700567, 27452623890, 602326265519, 14209892886819, 358576428141962, 9634718410829852, 274567642777650028, 8270000441627265937, 262464788618069324640, 8752908129221863491691, 305968679117675345995513 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 2..300 FORMULA a(n) = Sum_{k=1..n-1} A320264(n,k). a(n) = A257741(n) - A319518(n). EXAMPLE a(2) = 1: {a,a}. a(3) = 3: {a,a,a}, {a,a,b}, {a,b,b}. a(4) = 23: {a,a,a,a}, {a,a,aa}, {aa, aa}, {a,a,a,b}, {a,a,b,b}, {a,b,b,b}, {a,a,ab}, {a,a,ba}, {a,a,bb}, {b,b,ab}, {b,b,ba}, {b,b,aa}, {ab,ab}, {ba,ba}, {a,a,b,c}, {a,a,bc}, {a,a,cb}, {b,b,a,c}, {b,b,ac}, {b,b,ca}, {c,c,a,b}, {c,c,ab}, {c,c,ba}. MAPLE h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,       add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))     end: g:= proc(n, k) option remember; `if`(n=0, 1, add(add(       d*k^d, d=numtheory[divisors](j))*g(n-j, k), j=1..n)/n)     end: a:= n-> add(add((-1)^i*(g(n, k-i)-h(n\$2, k-i))*         binomial(k, i), i=0..k), k=1..n-1): seq(a(n), n=2..25); CROSSREFS Row sums of A320264. Cf. A257741, A319518. Sequence in context: A002398 A110065 A002816 * A144479 A074579 A060880 Adjacent sequences:  A320262 A320263 A320264 * A320266 A320267 A320268 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 08 2018 STATUS approved

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Last modified May 7 09:41 EDT 2021. Contains 343649 sequences. (Running on oeis4.)