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

0,3

Links

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

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. A058892, A215915.

Cf. A000041.

Sequence in context: A293723 A255807 A293916 * A254833 A342933 A275497

Adjacent sequences: A293728 A293729 A293730 * A293732 A293733 A293734

Keyword

nonn

Author

Seiichi Manyama, Oct 15 2017

Status

approved