A327828 Sum of multinomials M(n; lambda), where lambda ranges over all partitions of n into parts incorporating 2.

0, 0, 1, 3, 18, 100, 705, 5166, 44856, 413316, 4297635, 47906650, 586050828, 7669704978, 108433645502, 1632017808435, 26240224612920, 446861879976600, 8063224431751719, 153335328111105282, 3070484092409318100, 64508501542986638550, 1420061287311444508962

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450

Formula

a(n) ~ c * n!, where c = A247551/2 = 1.26473873603957632409005807712697712... - Vaclav Kotesovec, Sep 28 2019

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1,
     `if`(i>n, 0, b(n, i+1, `if`(i=k, 0, k))+
     `if`(i=k, 0, b(n-i, i, k)*binomial(n, i))))
    end:
a:= n-> b(n, 1, 0)-b(n, 1, 2):
seq(a(n), n=0..23);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i > n, 0, b[n, i + 1, If[i == k, 0, k]] + If[i == k, 0, b[n - i, i, k] Binomial[n, i]]]];
a[n_] := b[n, 1, 0] - b[n, 1, 2];
a /@ Range[0, 23] (* Jean-François Alcover, Dec 18 2020, after Alois P. Heinz *)

Crossrefs

Column k=2 of A327801.

Sequence in context: A321032 A180036 A038158 * A009021 A303519 A124408

Adjacent sequences: A327825 A327826 A327827 * A327829 A327830 A327831

Keyword

nonn

Author

Alois P. Heinz, Sep 26 2019

Status

approved