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A292190
Sum of n-th powers of products of terms in all partitions of n into distinct parts.
8
1, 1, 4, 35, 337, 11925, 371081, 49032439, 3545396034, 3416952655320, 749189363202730, 598250899004413536, 2383502427069445040595, 1729793152213690218766715, 131751643363739706679145099315, 271212858254426215135033141804302
OFFSET
0,3
LINKS
FORMULA
a(n) = [x^n] Product_{k=1..n} (1 + k^n*x^k).
EXAMPLE
5 = 4 + 1 = 3 + 2. So a(5) = 5^5 + (4*1)^5 + (3*2)^5 = 11925.
MAPLE
b:= proc(n, i, k) option remember; (m->
`if`(m<n, 0, `if`(n=m, i!^k, b(n, i-1, k)+
`if`(i>n, 0, i^k*b(n-i, i-1, k)))))(i*(i+1)/2)
end:
a:= n-> b(n$3):
seq(a(n), n=0..20); # Alois P. Heinz, Sep 11 2017
MATHEMATICA
nmax = 15; Table[SeriesCoefficient[Product[(1 + k^n*x^k), {k, 1, nmax}], {x, 0, n}], {n, 0, nmax}] (* Vaclav Kotesovec, Sep 12 2017 *)
PROG
(PARI) {a(n) = polcoeff(prod(k=1, n, 1+k^n*x^k+x*O(x^n)), n)}
CROSSREFS
Main diagonal of A292189.
Sequence in context: A174436 A145607 A188527 * A026304 A215541 A104456
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 11 2017
STATUS
approved