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URL: https://oeis.org/A106179

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A106179
Triangle read by rows: T(n,k) is the number of series-reduced planted trees with n leaves and k internal nodes.
2
1, 1, 1, 1, 2, 2, 1, 3, 5, 3, 1, 4, 10, 12, 6, 1, 5, 16, 29, 28, 11, 1, 6, 24, 57, 84, 66, 23, 1, 7, 33, 99, 192, 231, 157, 46, 1, 8, 44, 157, 382, 615, 634, 373, 98, 1, 9, 56, 234, 682, 1380, 1905, 1704, 890, 207, 1, 10, 70, 333, 1133, 2755, 4782, 5746, 4554, 2130, 451
OFFSET
2,5
REFERENCES
J. Riordan, The blossoming of Schroeder's fourth problem, Acta Math., 137 (1976), 1-16.
LINKS
FORMULA
A001678(n) = Sum_{i=2..n-2} T(i, n-1-i) for n >= 3. - Marko Riedel, Mar 29 2021
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 2;
1, 3, 5, 3;
1, 4, 10, 12, 6;
1, 5, 16, 29, 28, 11;
1, 6, 24, 57, 84, 66, 23;
1, 7, 33, 99, 192, 231, 157, 46;
1, 8, 44, 157, 382, 615, 634, 373, 98;
...
PROG
(PARI)
EulerMT(u)={my(n=#u, p=x*Ser(u), vars=variables(p)); Vec(exp( sum(i=1, n, substvec(p + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i ))-1)}
A(n)={my(v=vector(n)); v[1]=1; for(n=2, n, v[n]=y*EulerMT(v[1..n])[n]); apply(p -> Vecrev(p/y), v[2..n])}
{ my(T=A(10)); for(n=1, #T, print(T[n])) } \\ Andrew Howroyd, Sep 01 2018
CROSSREFS
Right diagonal is A001190.
Row sums give A000669.
Cf. A001678.
Sequence in context: A208336 A038137 A073133 * A081572 A292630 A144287
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, May 29 2005
EXTENSIONS
Name clarified and terms a(38) and beyond from Andrew Howroyd, Sep 01 2018
STATUS
approved