A360036 Expansion of e.g.f. x*exp(x)*(sinh(x))^2.

0, 0, 0, 6, 24, 100, 360, 1274, 4368, 14760, 49200, 162382, 531432, 1727180, 5580120, 17936130, 57395616, 182948560, 581130720, 1840247318, 5811307320, 18305618100, 57531942600, 180441092746, 564859072944, 1765184603000, 5507375961360, 17157594341214, 53379182394888

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 have an odd number of elements and an element is selected from the third.

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (6,-7,-12,17,6,-9).

Formula

a(n) = n*A081251(n-2) for n >= 3.

a(n) = n*(3^(n-1) + (-1)^(n-1) - 2)/4.

G.f.: 2*x^3*(3 - 6*x - x^2)/((1 - x)^2*(1 + x)^2*(1 - 3*x)^2). - Stefano Spezia, Jan 23 2023

Example

The first 4 cases are shown below for a(4)=24 (where the element selected from the third set is in parenthesis):
{1}, {2}, {(3), 4}
{1}, {2}, {3, (4)}
{2}, {1}, {(3), 4}
{2}, {1}, {3, (4)}.

Crossrefs

Cf. A081251, A015518, A360023, A360035.

Sequence in context: A037688 A378497 A343116 * A255471 A126393 A265697

Adjacent sequences: A360033 A360034 A360035 * A360037 A360038 A360039

Keyword

nonn,easy

Author

Enrique Navarrete, Jan 22 2023

Status

approved