login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A327826 Sum of multinomials M(n; lambda), where lambda ranges over all partitions of n into parts that form a set of size two. 2
0, 0, 0, 3, 16, 125, 711, 5915, 46264, 438681, 4371085, 49321745, 588219523, 7751724513, 108240044745, 1633289839823, 26102966544024, 445098171557393, 8006283582196761, 152353662601600853, 3046062181913575921, 64015245150903376151, 1408108698825029286195 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

Wikipedia, Multinomial coefficients

Wikipedia, Partition (number theory)

FORMULA

a(n) ~ c * n!, where c = Sum_{k>=2} 1/(k! - 1) = 1.253498755699953471643360937905798940369232208332... - Vaclav Kotesovec, Sep 28 2019, updated Jul 19 2021

MAPLE

with(combinat):

b:= proc(n, i) option remember; series(`if`(n=0, 1,

     `if`(i<1, 0, add(x^signum(j)*b(n-i*j, i-1)*

      multinomial(n, n-i*j, i$j), j=0..n/i))), x, 3)

    end:

a:= n-> coeff(b(n$2), x, 2):

seq(a(n), n=0..25);

MATHEMATICA

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

b[n_, i_] := b[n, i] = Series[If[n == 0, 1, If[i < 1, 0, Sum[x^Sign[j] b[n - i*j, i - 1] multinomial[n, Join[{n - i*j}, Table[i, {j}]]], {j, 0, n/i}]]], {x, 0, 3}];

a[n_] := SeriesCoefficient[b[n, n], {x, 0, 2}];

a /@ Range[0, 25] (* Jean-Fran├žois Alcover, Dec 18 2020, after Alois P. Heinz *)

CROSSREFS

Column k=2 of A327803.

Sequence in context: A090135 A351423 A188417 * A157457 A000950 A320254

Adjacent sequences:  A327823 A327824 A327825 * A327827 A327828 A327829

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 26 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 12 07:45 EDT 2022. Contains 356067 sequences. (Running on oeis4.)