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A055363 Triangle of asymmetric mobiles (circular rooted trees) with n nodes and k leaves. 12
1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 4, 4, 1, 0, 0, 1, 6, 10, 5, 1, 0, 0, 1, 9, 22, 19, 7, 1, 0, 0, 1, 12, 42, 53, 31, 8, 1, 0, 0, 1, 16, 73, 130, 109, 45, 10, 1, 0, 0, 1, 20, 119, 280, 321, 190, 63, 11, 1, 0, 0, 1, 25, 184, 556, 833, 672, 310, 83, 13, 1, 0, 0, 1, 30, 272 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,12

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)

Index entries for sequences related to mobiles

FORMULA

G.f. satisfies A(x, y) = x*(y - Sum_{i>0} moebius(i)/i * log(1 - A(x^i, y^i))). - Michael Somos, Aug 19 2015

Sum_k T(n, k) = A032171(n). - Michael Somos, Aug 24 2015

EXAMPLE

G.f. = x*(y + x*y + x^2*y + x^3*(y + y^2) + x^4*(y + 2*y^2 + y^3) + x^5*(y + 4*y^2 + 4*y^3 + y^4) + ...).

n\k 1  2  3  4  5  6  7  8

--:-- -- -- -- -- -- -- --

1:  1

2:  1  0

3:  1  0  0

4:  1  1  0  0

5:  1  2  1  0  0

6:  1  4  4  1  0  0

7:  1  6 10  5  1  0  0

8:  1  9 22 19  7  1  0  0

MATHEMATICA

T[n_, k_] := Module[{A}, A[_, _] = 0; If[k<1 || k>n, 0, For[j=1, j <= n, j++, A[x_, y_] = x*y-x*Sum[MoebiusMu[i]/i * Log[1 - A[x^i, y^i]] + O[x]^j // Normal, {i, 1, j}]]; Coefficient[Coefficient[A[x, y], x, n], y, k]]];

Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Jean-Fran├žois Alcover, Jun 30 2017, after Michael Somos *)

PROG

(PARI) {T(n, k) = my(A = O(x)); if(k<1 || k>n, 0, for(j=1, n, A = x*y - x*sum(i=1, j, moebius(i)/i * log(1 - subst( subst( A + x * O(x^min(j, n\i)), x, x^i), y, y^i) ) )); polcoeff( polcoeff(A, n), k))}; /* Michael Somos, Aug 24 2015 */

CROSSREFS

Row sums give A032171.

Columns 2..8: A002620(n-2), A055364, A055365, A055366, A055367, A055368, A055369.

Cf. A055340, A055349, A055356, A055370, A055371.

Sequence in context: A188816 A168312 A076837 * A350681 A110855 A054673

Adjacent sequences:  A055360 A055361 A055362 * A055364 A055365 A055366

KEYWORD

nonn,tabl

AUTHOR

Christian G. Bower, May 15 2000

STATUS

approved

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Last modified May 16 15:15 EDT 2022. Contains 353706 sequences. (Running on oeis4.)