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 A306027 Number of length-n restricted growth strings (RGS) with growth <= three and first element in [3]. 3
 1, 3, 15, 95, 717, 6221, 60619, 652595, 7667957, 97415437, 1328078067, 19310628827, 297932883437, 4856255827013, 83315165338923, 1499606140412403, 28237439054261893, 554849548137840189, 11351488777441797187, 241314920928367232747, 5320846918247724517117 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..481 FORMULA E.g.f.: exp(Sum_{j=1..3} (exp(j*x)-1)/j). EXAMPLE a(2) = 15: 11, 12, 13, 14, 21, 22, 23, 24, 25, 31, 32, 33, 34, 35, 36. MAPLE b:= proc(n, m) option remember; `if`(n=0, 1,       add(b(n-1, max(m, j)), j=1..m+3))     end: a:= n-> b(n, 0): seq(a(n), n=0..25); # second Maple program: a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..3)), x, n+1), x, n): seq(a(n), n=0..25); CROSSREFS Column k=3 of A306024. Cf. A189845. Sequence in context: A274734 A177341 A220262 * A304072 A076301 A112913 Adjacent sequences:  A306024 A306025 A306026 * A306028 A306029 A306030 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 17 2018 STATUS approved

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Last modified January 18 17:18 EST 2022. Contains 350455 sequences. (Running on oeis4.)