1,2

a(n,m) enumerates unordered n-vertex m-forests composed of m plane increasing 8-ary trees. See the F. Bergeron et al. reference, especially Table 1, first row, for the e.g.f. for m=1.

a(n,m) := S2(8; n,m) is the eighth triangle of numbers in the sequence S2(k;n,m), k=1..7: A008277 (unsigned Stirling 2nd kind), A008297 (unsigned Lah), A035342, A035469, A049029, A049385, A092082, respectively. a(n,1)=A045754(n), n>=1.

F. Bergeron, Ph. Flajolet and B. Salvy, Varieties of Increasing Trees, in Lecture Notes in Computer Science vol. 581, ed. J.-C. Raoult, Springer 1922, pp. 24-48.

P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem.

W. Lang, First 10 rows.

a(n, m) = n!*A132057(n, m)/(m!*7^(n-m)); a(n+1, m) = (7*n+m)*a(n, m)+ a(n, m-1), n >= m >= 1; a(n, m) := 0, n<m; a(n, 0) := 0, a(1, 1)=1;

E.g.f. of m-th column: ((-1+(1-7*x)^(-1/7))^m)/m!.

a(n, m) = sum(|A051186(n, j)|*S2(j, m), j=m..n) (matrix product), with S2(j, m):= (j, m) (Stirling2 triangle). Priv. comm. with W. Lang by E. Neuwirth, Feb 15 2001; see also the 2001 Neuwirth reference. See the general comment on products of Jabotinsky matrices given under A035342.

{1}; {8,1}; {120,24,1}; {2640,672,48,1}; ...

Cf. A132060 (row sums), A132061 (alternating row sums).

Cf. A092082 S2(7) triangle.

Sequence in context: A143499 A114152 A048786 this_sequence A051187 A021850 A011105

Adjacent sequences: A132053 A132054 A132055 this_sequence A132057 A132058 A132059

nonn,easy,tabl

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Sep 14 2007