A360588 Expansion of e.g.f. (exp(x)-1)^2*(x+x^2/2).

0, 0, 0, 6, 36, 130, 390, 1064, 2744, 6822, 16530, 39292, 92004, 212810, 487214, 1105680, 2490096, 5570254, 12385962, 27393668, 60292700, 132120114, 288357894, 627047896, 1358953896, 2936012150, 6325009730, 13589544204, 29125246164, 62277024922, 132875549790, 282930969632, 601295420384

Offset

0,4

Comments

a(n) is the number of ordered set partitions of an n-set into 3 sets such that the first and second sets contain at least one element and the third set contains either one or two elements.

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (9,-33,63,-66,36,-8).

Formula

a(n) = n*2^(n-1) + binomial(n,2)*(2^(n-2)-2) - 2*n, n >= 3, a(n) = 0 otherwise.

Example

a(5)=130 since the set partitions are the following:
  20 of the form {1,2,3}, {4}, {5};
  20 of the form {1}, {2,3,4}, {5};
  30 of the form {1,2}, {3,4}, {5};
  30 of the form {1,2}, {3}, {4,5};
  30 of the form {1}, {2,3}, {4,5}.

Prog

(PARI) a(n) = if (n>=3, n*2^(n-1) + binomial(n, 2)*(2^(n-2)-2) - 2*n, 0); \\ Michel Marcus, Feb 13 2023

Crossrefs

Sequence in context: A253945 A331576 A056375 * A321579 A364429 A018214

Adjacent sequences: A360585 A360586 A360587 * A360589 A360590 A360591

Keyword

nonn,easy

Author

Enrique Navarrete, Feb 12 2023

Status

approved