A293731 E.g.f.: exp(Sum_{n>=1} n*A000041(n)*x^n), where A000041(n) is the number of partitions of n.

1, 1, 9, 79, 937, 12501, 204361, 3703099, 76460049, 1732292137, 43118784361, 1161659388231, 33771008443129, 1050438417598909, 34839221780655657, 1225699869182970931, 45592202322141065761, 1786608566424333658449, 73553912374465725486409

Offset: 0

Author

Seiichi Manyama, Oct 15 2017

Keywords

• nonn

Examples

			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.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..410

Crossrefs

Cf. A058892, A215915.

Cf. A000041.

Programs

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 *)

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.