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 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 Alois P. Heinz, Table of n, a(n) for n = 0..30 Wikipedia, Multinomial coefficients 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 Adjacent sequences: A326318 A326319 A326320 * A326322 A326323 A326324 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 11 2019 STATUS approved

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Last modified June 12 10:29 EDT 2024. Contains 373331 sequences. (Running on oeis4.)