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 A306024 Number A(n,k) of length-n restricted growth strings (RGS) with growth <= k and first element in [k]; square array A(n,k), n>=0, k>=0, read by antidiagonals. 13
 1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 3, 7, 5, 0, 1, 4, 15, 31, 15, 0, 1, 5, 26, 95, 164, 52, 0, 1, 6, 40, 214, 717, 999, 203, 0, 1, 7, 57, 405, 2096, 6221, 6841, 877, 0, 1, 8, 77, 685, 4875, 23578, 60619, 51790, 4140, 0, 1, 9, 100, 1071, 9780, 67354, 297692, 652595, 428131, 21147, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS A(n,k) counts strings [s_1, ..., s_n] with 1 <= s_i <= k + max(0, max_{j b(n, k, 0): seq(seq(A(n, d-n), n=0..d), d=0..12); # second Maple program: A:= (n, k)-> n!*coeff(series(exp(add(     (exp(j*x)-1)/j, j=1..k)), x, n+1), x, n): seq(seq(A(n, d-n), n=0..d), d=0..12); 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_, k_] := b[n, k, 0]; Table[A[n, d-n], {d, 0, 12}, {n, 0, d}] // Flatten (* Jean-François Alcover, May 27 2019, after Alois P. Heinz *) CROSSREFS Columns k=0-10 give: A000007, A000110, A002872, A306027, A306028, A306029, A306030, A306031, A306032, A306033, A306034. Main diagonal gives A306025. Antidiagonal sums give A306026. Cf. A305962. Sequence in context: A261780 A124540 A124550 * A237018 A290605 A292913 Adjacent sequences:  A306021 A306022 A306023 * A306025 A306026 A306027 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Jun 17 2018 STATUS approved

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Last modified March 28 20:44 EDT 2020. Contains 333103 sequences. (Running on oeis4.)