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 A305963 Number of length-n restricted growth strings (RGS) with growth <= n and fixed first element. 3
 1, 1, 3, 22, 305, 6756, 216552, 9416240, 530764089, 37498693555, 3235722405487, 334075729235172, 40587204883652869, 5722676826879812177, 925590727478445526747, 170032646641380554970304, 35173161711207720944899921, 8132124409499796317194563900 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..266 FORMULA a(n) = (n-1)! * [x^(n-1)] exp(x + Sum_{j=1..n} (exp(j*x)-1)/j) for n > 0, a(0) = 1. a(n) = A305962(n,n). EXAMPLE a(2) = 3: 11, 12, 13. a(3) = 22: 111, 112, 113, 114, 121, 122, 123, 124, 125, 131, 132, 133, 134, 135, 136, 141, 142, 143, 144, 145, 146, 147. MAPLE b:= proc(n, k, m) option remember; `if`(n=0, 1, add(b(n-1, k, max(m, j)), j=1..m+k)) end: a:= n-> b(n\$2, 1-n): seq(a(n), n=0..20); # second Maple program: a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add( (exp(j*x)-1)/j, j=1..n)), x, n), x, n-1)): seq(a(n), n=0..20); MATHEMATICA b[n_, k_, m_] := b[n, k, m] = If[n == 0, 1, Sum[b[n - 1, k, Max[m, j]], {j, 1, m + k}]]; a[n_] := b[n, n, 1 - n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 21 2022, after Alois P. Heinz *) CROSSREFS Main diagonal of A305962. Cf. A306025. Sequence in context: A119390 A271848 A144681 * A261280 A124567 A161967 Adjacent sequences: A305960 A305961 A305962 * A305964 A305965 A305966 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 15 2018 STATUS approved

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Last modified January 29 14:44 EST 2023. Contains 359923 sequences. (Running on oeis4.)