A271743 Number of set partitions of [n] such that 4 is the largest element of the last block.

10, 15, 29, 63, 149, 375, 989, 2703, 7589, 21735, 63149, 185343, 547829, 1627095, 4848509, 14479983, 43308869, 129664455, 388469069, 1164358623, 3490978709, 10468741815, 31397836829, 94176733263, 282496645349, 847422827175, 2542134263789, 7626134355903

Offset

4,1

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 (6,-11,6).

Formula

G.f.: x^4*(3*x-2)*(2*x^2-15*x+5)/Product_{j=1..3} (j*x-1).

From Colin Barker, May 21 2017: (Start)

G.f.: x^4*(2 - 3*x)*(5 - 15*x + 2*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).

a(n) = 4 + 2^(n-2) + 3^(n-4) for n>4.

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>7.

(End)

Example

a(4) = 10: 1234, 123|4, 12|34, 12|3|4, 13|24, 13|2|4, 1|234, 1|23|4, 1|2|34, 1|2|3|4.

Mathematica

Join[{10}, LinearRecurrence[{6, -11, 6}, {15, 29, 63}, 30]] (* Vincenzo Librandi, Apr 13 2016 *)

Prog

(Magma) I:=[10, 15, 29, 63]; [n le 4 select I[n] else 6*Self(n-1) -11*Self(n-2)+6*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Apr 13 2016
(PARI) Vec(x^4*(2 - 3*x)*(5 - 15*x + 2*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)) + O(x^40)) \\ Colin Barker, May 21 2017

Crossrefs

Column k=4 of A271466.

Sequence in context: A254362 A182427 A171956 * A060535 A239595 A037379

Adjacent sequences: A271740 A271741 A271742 * A271744 A271745 A271746

Keyword

nonn,easy

Author

Alois P. Heinz, Apr 13 2016

Status

approved