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

Author

Alois P. Heinz, Apr 13 2016

Keywords

• nonn
• easy

Examples

			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.
		

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).

Crossrefs

Column k=4 of A271466.

Programs

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

Mathematica

Join[{10},LinearRecurrence[{6,-11,6},{15,29,63},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

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)