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A293731
E.g.f.: exp(Sum_{n>=1} n*A000041(n)*x^n), where A000041(n) is the number of partitions of n.
3
1, 1, 9, 79, 937, 12501, 204361, 3703099, 76460049, 1732292137, 43118784361, 1161659388231, 33771008443129, 1050438417598909, 34839221780655657, 1225699869182970931, 45592202322141065761, 1786608566424333658449, 73553912374465725486409
OFFSET
0,3
LINKS
FORMULA
a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} k^2*A000041(k)*a(n-k)/(n-k)! for n > 0.
EXAMPLE
a(5) = 4! * (1^2*1*a(4)/4! + 2^2*2*a(3)/3! + 3^2*3*a(2)/2! + 4^2*5*a(1)/1! + 5^2*7*a(0)/0!) = 12501.
MATHEMATICA
nmax = 20; CoefficientList[Series[E^Sum[k*PartitionsP[k]*x^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 18 2017 *)
CROSSREFS
Cf. A000041.
Sequence in context: A293723 A255807 A293916 * A254833 A342933 A275497
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 15 2017
STATUS
approved