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A330778 Triangle read by rows: T(n,k) is the number of balanced reduced multisystems of weight n with maximum depth and atoms colored using exactly k colors. 2
1, 1, 1, 1, 4, 3, 2, 17, 33, 18, 5, 86, 321, 420, 180, 16, 520, 3306, 7752, 7650, 2700, 61, 3682, 37533, 140172, 238560, 189000, 56700, 272, 30050, 473604, 2644356, 6899070, 9196740, 6085800, 1587600, 1385, 278414, 6630909, 53244180, 199775820, 398328480, 435954960, 247665600, 57153600 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

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

EXAMPLE

Triangle begins:

    1;

    1,     1;

    1,     4,      3;

    2,    17,     33,      18;

    5,    86,    321,     420,     180;

   16,   520,   3306,    7752,    7650,    2700;

   61,  3682,  37533,  140172,  238560,  189000,   56700;

  272, 30050, 473604, 2644356, 6899070, 9196740, 6085800, 1587600;

  ...

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, for(i=n, #v, u[i] += v[i]*(-1)^(i-n)*binomial(i-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 A000111.

Main diagonal is A006472.

Row sums are A330676.

Cf. A330776.

Sequence in context: A319541 A239020 A293211 * A061312 A019130 A245348

Adjacent sequences:  A330775 A330776 A330777 * A330779 A330780 A330781

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Dec 30 2019

STATUS

approved

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Last modified August 13 05:41 EDT 2020. Contains 336442 sequences. (Running on oeis4.)