login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A330776 Triangle read by rows: T(n,k) is the number of balanced reduced multisystems of weight n with atoms colored using exactly k colors. 3
1, 1, 1, 2, 6, 4, 6, 37, 63, 32, 20, 262, 870, 1064, 436, 90, 2217, 12633, 27824, 26330, 9012, 468, 21882, 201654, 710712, 1163320, 895608, 262760, 2910, 249852, 3578610, 18924846, 47608000, 61786254, 40042128, 10270696, 20644, 3245520, 70539124, 538018360, 1950556400, 3792461176, 4070160416, 2275829088, 518277560 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

See A330655 for the definition of a balanced reduced multisystem.

A balanced reduced multisystem of weight n with atoms of k colors corresponds with a rooted tree with n leaves of k colors with all leaves at the same depth and at least one node at each level of the tree having more than one child. The final condition is needed to ensure that the number of such trees is finite.

LINKS

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

EXAMPLE

Triangle begins:

    1;

    1,     1;

    2,     6,      4;

    6,    37,     63,     32;

   20,   262,    870,   1064,     436;

   90,  2217,  12633,  27824,   26330,   9012;

  468, 21882, 201654, 710712, 1163320, 895608, 262760;

  ...

The T(3,2) = 6 balanced reduced multisystems are: {1,1,2}, {1,2,2}, {{1},{1,2}}, {{1},{2,2}}, {{2},{1,1}}, {{2},{1,2}}.

PROG

(PARI)

EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}

R(n, k)={my(v=vector(n), u=vector(n)); v[1]=k; for(n=1, #v, u += v*sum(j=n, #v, (-1)^(j-n)*binomial(j-1, n-1)); v=EulerT(v)); u}

M(n)={my(v=vector(n, k, R(n, k)~)); Mat(vector(n, k, sum(i=1, k, (-1)^(k-i)*binomial(k, i)*v[i])))}

{my(T=M(10)); for(n=1, #T~, print(T[n, 1..n]))}

CROSSREFS

Column 1 is A318813.

Main diagonal is A005121.

Row sums are A330655.

Sequence in context: A151689 A216833 A242046 * A327458 A202347 A266120

Adjacent sequences:  A330773 A330774 A330775 * A330777 A330778 A330779

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Dec 30 2019

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 22 13:36 EDT 2020. Contains 337289 sequences. (Running on oeis4.)