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 A244461 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 7. 3
 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 4, 7, 12, 16, 21, 25, 30, 38, 52, 74, 108, 151, 206, 271, 356, 468, 629, 855, 1180, 1620, 2212, 2991, 4030, 5420, 7320, 9922, 13508, 18396, 25049, 34032, 46194, 62653, 85051, 115548, 157168, 213852, 291046, 395990 (list; graph; refs; listen; history; text; internal format)
 OFFSET 8,9 LINKS Alois P. Heinz, Table of n, a(n) for n = 8..900 MAPLE b:= proc(n, i, t, k) option remember; `if`(n=0, `if`(t in [0, k], 1, 0), `if`(i<1 or t>n, 0, add(binomial(b((i-1)\$2, k\$2)+j-1, j)* b(n-i*j, i-1, max(0, t-j), k), j=0..n/i))) end: a:= n-> b(n-1\$2, 7\$2) -b(n-1\$2, 8\$2): seq(a(n), n=8..65); MATHEMATICA b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]*b[n - i*j, i - 1, Max[0, t - j], k], {j, 0, n/i}]] // FullSimplify]; a[n_] := b[n - 1, n - 1, 7, 7] - b[n - 1, n - 1, 8, 8]; Table[a[n], {n, 8, 65}] (* Jean-François Alcover, Feb 06 2015, after Maple *) CROSSREFS Column k=7 of A244454. Cf. A244536. Sequence in context: A202709 A279611 A008767 * A366811 A343925 A105255 Adjacent sequences: A244458 A244459 A244460 * A244462 A244463 A244464 KEYWORD nonn AUTHOR Joerg Arndt and Alois P. Heinz, Jun 29 2014 STATUS approved

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Last modified December 9 13:48 EST 2023. Contains 367691 sequences. (Running on oeis4.)