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 A301368 Regular triangle where T(n,k) is the number of binary enriched p-trees of weight n with k leaves. 9
 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 2, 4, 5, 3, 1, 3, 7, 12, 12, 6, 1, 3, 9, 19, 28, 25, 11, 1, 4, 14, 36, 65, 81, 63, 24, 1, 4, 16, 48, 107, 172, 193, 136, 47, 1, 5, 22, 75, 192, 369, 522, 522, 331, 103, 1, 5, 25, 96, 284, 643, 1108, 1420, 1292, 750, 214, 1, 6 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS A binary enriched p-tree of weight n is either a single node of weight n, or an ordered pair of binary enriched p-trees with weakly decreasing weights summing to n. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 EXAMPLE Triangle begins:   1   1   1   1   1   1   1   2   3   2   1   2   4   5   3   1   3   7  12  12   6   1   3   9  19  28  25  11   1   4  14  36  65  81  63  24   1   4  16  48 107 172 193 136  47   1   5  22  75 192 369 522 522 331 103   ... The T(6,3) = 7 binary enriched p-trees: ((41)1), ((32)1), (4(11)), ((31)2), ((22)2), (3(21)), ((21)3). MATHEMATICA bintrees[n_]:=Prepend[Join@@Table[Tuples[bintrees/@ptn], {ptn, Select[IntegerPartitions[n], Length[#]===2&]}], n]; Table[Length[Select[bintrees[n], Count[#, _Integer, {-1}]===k&]], {n, 13}, {k, n}] PROG (PARI) A(n)={my(v=vector(n)); for(n=1, n, v[n] = y + sum(k=1, n\2, v[k]*v[n-k])); apply(p->Vecrev(p/y), v)} { my(T=A(10)); for(n=1, #T, print(T[n])) } \\ Andrew Howroyd, Aug 26 2018 CROSSREFS Last entries of each row give A000992. Row sums are A300443. Cf. A001190, A008284, A055277, A063834, A196545, A273873, A289501, A292050, A298422, A298426, A300354, A300439, A300442, A301344, A301364-A301367. Sequence in context: A245436 A285581 A222173 * A198242 A049063 A120894 Adjacent sequences:  A301365 A301366 A301367 * A301369 A301370 A301371 KEYWORD nonn,tabl AUTHOR Gus Wiseman, Mar 19 2018 STATUS approved

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Last modified May 7 20:36 EDT 2021. Contains 343652 sequences. (Running on oeis4.)