The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A326321 Sum of the n-th powers of multinomials M(n; mu), where mu ranges over all compositions of n. 4
1, 1, 5, 271, 395793, 28076306251, 150414812114874563, 86530666539373619904011413, 7177587537701279221012034803727966465, 110824376322428312270365608303690048162629868273811, 399431453468560513224979712848478555015392084082614167438553312275 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
From Vaclav Kotesovec, Sep 14 2019: (Start)
a(n) ~ (n!)^n.
a(n) ~ 2^(n/2) * Pi^(n/2) * n^(n*(2*n+1)/2) / exp(n^2-1/12). (End)
a(n) = (n!)^n * [x^n] 1 / (1 - Sum_{k>=1} x^k / (k!)^n). - Ilya Gutkovskiy, Jul 11 2020
EXAMPLE
a(2) = M(2; 2)^2 + M(2; 1,1)^2 = 1 + 4 = 5.
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1,
add(b(n-i, k)/i!^k, i=1..n))
end:
a:= n-> n!^n*b(n$2):
seq(a(n), n=0..12);
# second Maple program:
b:= proc(n, k) option remember; `if`(n=0, 1,
add(binomial(n, j)^k*b(j, k), j=0..n-1))
end:
a:= n-> b(n$2):
seq(a(n), n=0..10);
MATHEMATICA
b[n_, k_] := b[n, k] = If[n==0, 1, Sum[Binomial[n, j]^k b[j, k], {j, 0, n-1}]];
a[n_] := b[n, n];
a /@ Range[0, 10] (* Jean-François Alcover, Dec 03 2020, after 2nd Maple program *)
CROSSREFS
Main diagonal of A326322.
Cf. A215910.
Sequence in context: A329610 A283518 A153322 * A234324 A066210 A036213
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 11 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 June 12 10:29 EDT 2024. Contains 373331 sequences. (Running on oeis4.)