A305778 Number of set partitions of [n] with alternating parity of elements and exactly four blocks.

1, 4, 12, 33, 84, 222, 545, 1425, 3458, 8948, 21595, 55335, 133144, 338530, 813249, 2056245, 4935870, 12432432, 29833463, 74952867, 179842724, 451071998, 1082309293, 2711584785, 6506473162, 16289249356, 39088013091, 97811687679, 234720639024, 587166227226

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Wikipedia, Partition of a set

Index entries for linear recurrences with constant coefficients, signature (1,18,-18,-127,127,450,-450,-844,844,792,-792,-288,288)

Formula

G.f.: (72*x^11 -84*x^10 -258*x^9 +60*x^8 +287*x^7 +29*x^6 -141*x^5 -34*x^4 +33*x^3 +10*x^2 -3*x-1) *x^4 / ((2*x+1) *(2*x-1) *(x+1) *(6*x^2-1) *(3*x^2-1) *(x-1)^2 *(2*x^2-1)^2).

Example

a(5) = 4: 12|3|4|5, 1|23|4|5, 1|2|34|5, 1|2|3|45.

Crossrefs

Column k=4 of A274581.

Sequence in context: A225894 A318637 A227554 * A343561 A104747 A070050

Adjacent sequences: A305775 A305776 A305777 * A305779 A305780 A305781

Keyword

nonn,easy

Author

Alois P. Heinz, Jun 10 2018

Status

approved