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A271715 Number of set partitions of [3n] with minimal block length multiplicity equal to n. 2
1, 4, 55, 1540, 67375, 4239235, 383563180, 51925673800, 10652498631775, 3139051466175625, 1228555090548911125, 602267334323068414000, 357161594247065690582500, 250870551734754490461422500, 205672479804595549379158525000, 194557626586812183102927448930000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

a(n) = A271424(3n,n).

Recursion: see Maple program.

For n>0, a(n) = (3^n + n!)*(3*n)! / (6^n * (n!)^2). - Vaclav Kotesovec, Apr 16 2016

MAPLE

a:= proc(n) option remember; `if`(n<5,

      [1, 4, 55, 1540, 67375][n+1], ((2*(3*n-2))*

       (3*n-1)*(n^2-n-9)*a(n-1) -(3*(n-3))*(3*n-1)*

       (3*n-4)*(3*n-2)*(3*n-5)*a(n-2))/(4*n*(n-4)))

    end:

seq(a(n), n=0..20);

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!);

b[n_, i_, k_] := b[n, i, k] = If[n==0, 1, If[i<1, 0, Sum[multinomial[n, Join[{n - i*j}, Array[i&, j]]]*b[n - i*j, i - 1, k]/j!, {j, Join[{0}, Range[k, n/i]] // Union}]]];

a[n_] := If[n==0, 1, b[3n, 3n, n] - b[3n, 3n, n+1]];

a /@ Range[0, 20] (* Jean-Fran├žois Alcover, Dec 11 2020, after Alois P. Heinz in A271424 *)

CROSSREFS

Cf. A271424.

Sequence in context: A195634 A322627 A206384 * A099122 A001500 A246968

Adjacent sequences:  A271712 A271713 A271714 * A271716 A271717 A271718

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 12 2016

STATUS

approved

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Last modified January 24 13:48 EST 2022. Contains 350538 sequences. (Running on oeis4.)