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 A301364 Regular triangle where T(n,k) is the number of enriched p-trees of weight n with k leaves. 10
 1, 1, 1, 1, 1, 2, 1, 2, 4, 5, 1, 2, 6, 11, 12, 1, 3, 10, 26, 38, 34, 1, 3, 13, 39, 87, 117, 92, 1, 4, 19, 69, 181, 339, 406, 277, 1, 4, 23, 95, 303, 707, 1198, 1311, 806, 1, 5, 30, 143, 514, 1430, 2970, 4525, 4522, 2500, 1, 5, 35, 184, 762, 2446, 6124, 11627 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS An enriched p-tree of weight n > 0 is either a single node of weight n, or a finite sequence of two or more 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   2   1   2   4   5   1   2   6  11  12   1   3  10  26  38  34   1   3  13  39  87 117  92   1   4  19  69 181 339 406 277   ... The T(5,4) = 11 enriched p-trees: (((21)1)1), ((2(11))1), (((11)2)1), ((211)1), ((21)(11)), (((11)1)2), ((111)2), ((21)11), (2(11)1), ((11)21), (2111). MATHEMATICA eptrees[n_]:=Prepend[Join@@Table[Tuples[eptrees/@ptn], {ptn, Select[IntegerPartitions[n], Length[#]>1&]}], n]; Table[Length[Select[eptrees[n], Count[#, _Integer, {-1}]===k&]], {n, 8}, {k, n}] PROG (PARI) A(n)={my(v=vector(n)); for(n=1, n, v[n] = y + polcoef(1/prod(k=1, n-1, 1 - v[k]*x^k + O(x*x^n)), n)); 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 A196545. Row sums are A289501. Cf. A008284, A055277, A063834, A220418, A273866, A273873, A281145, A290261, A299201, A299202, A299203, A300354, A300442, A300443, A301365-A301368. Sequence in context: A256188 A072727 A292601 * A309503 A057061 A307729 Adjacent sequences:  A301361 A301362 A301363 * A301365 A301366 A301367 KEYWORD nonn,tabl AUTHOR Gus Wiseman, Mar 19 2018 STATUS approved

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Last modified April 11 18:00 EDT 2021. Contains 342888 sequences. (Running on oeis4.)