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A219565 Number of 5-partite partitions of (n,n,n,n,n) into distinct quintuples. 4
1, 52, 6995, 937776, 107652681, 10781201973, 958919976957, 76861542428397, 5620227129073491, 378709513816248475, 23713852762539359688, 1389561695379881634055, 76647024053735036288641, 3999799865715906390697377, 198328846122797866982616805, 9379277765981012067789260214 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of factorizations of (p*q*r*s*t)^n into distinct factors where p, q, r, s, t are distinct primes.

LINKS

Table of n, a(n) for n=0..15.

FORMULA

a(n) = [(v*w*x*y*z)^n] 1/2 * Product_{h,i,j,k,m>=0} (1+v^h*w^i*x^j*y^k*z^m).

MATHEMATICA

a[n_] := a[n] = If[n == 0, 1, (1/2) Coefficient[Product[O[v]^(n+1) + O[w]^(n+1) + O[x]^(n+1) + O[y]^(n+1) + O[z]^(n+1) + (1 + v^i w^j x^k y^l z^m), {i, 0, n}, {j, 0, n}, {k, 0, n}, {l, 0, n}, {m, 0, n}] // Normal, (v w x y z)^n]];

Table[Print[n, " ", a[n]]; a[n], {n, 0, 7}] (* Jean-Fran├žois Alcover, Sep 24 2019 *)

CROSSREFS

Column k=5 of A219585.

Cf. A002774, A219554, A219560, A219561.

Sequence in context: A200576 A295450 A306283 * A294507 A209500 A093252

Adjacent sequences:  A219562 A219563 A219564 * A219566 A219567 A219568

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 23 2012

EXTENSIONS

a(6) from Alois P. Heinz, Sep 25 2014

a(7)-a(15) from Andrew Howroyd, Dec 16 2018

STATUS

approved

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Last modified June 28 12:59 EDT 2022. Contains 354907 sequences. (Running on oeis4.)