login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A227774 Triangular array read by rows: T(n,k) is the number of rooted identity trees with n nodes having exactly k subtrees from the root. 10
1, 1, 1, 1, 1, 2, 1, 3, 3, 6, 5, 1, 12, 11, 2, 25, 22, 5, 52, 49, 12, 113, 104, 28, 2, 247, 232, 65, 4, 548, 513, 152, 13, 1226, 1159, 351, 34, 2770, 2619, 818, 91, 1, 6299, 5989, 1907, 225, 6, 14426, 13734, 4460, 571, 18, 33209, 31729, 10453, 1403, 57, 76851 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Row sums = A004111.

LINKS

Alois P. Heinz, Rows n = 1..400, flattened

FORMULA

G.f.: x * Product_{n>=1} (1 + y * x^n)^A004111(n).

EXAMPLE

Triangular array T(n,k) begins:

1;

.   1;

.   1;

.   1,   1;

.   2,   1;

.   3,   3;

.   6,   5,  1;

.  12,  11,  2;

.  25,  22,  5;

.  52,  49, 12;

. 113, 104, 28, 2;

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(binomial(b((i-1)$2), j)*b(n-i*j, i-1), j=0..n/i)))

    end:

g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, expand(

      add(x^j*binomial(b((i-1)$2), j)*g(n-i*j, i-1), j=0..n/i))))

    end:

T:= n-> `if`(n=1, 1,

    (p-> seq(coeff(p, x, k), k=1..degree(p)))(g((n-1)$2))):

seq(T(n), n=1..25);  # Alois P. Heinz, Jul 30 2013

MATHEMATICA

nn=20; f[x_]:=Sum[a[n]x^n, {n, 0, nn}]; sol=SolveAlways[0==Series[f[x]-x Product[(1+x^i)^a[i], {i, 1, nn}], {x, 0, nn}], x]; A004111=Drop[ Flatten[Table[a[n], {n, 0, nn}]/.sol], 1]; Map[Select[#, #>0&]&, Drop[CoefficientList[Series[x Product[(1 + y x^i)^A004111[[i]], {i, 1, nn}], {x, 0, nn}], {x, y}], 1]]//Grid

CROSSREFS

Columns k=1-10 give: A004111(n-1), A227806, A227807, A227808, A227809, A227810, A227811, A227812, A227813, A227814.

Sequence in context: A213934 A124774 A056610 * A214920 A096373 A216961

Adjacent sequences:  A227771 A227772 A227773 * A227775 A227776 A227777

KEYWORD

nonn,tabf,look

AUTHOR

Geoffrey Critzer, Jul 30 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 16 13:42 EDT 2017. Contains 290623 sequences.