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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 (list; graph; refs; listen; history; text; internal format)
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 A275497 A171314

Adjacent sequences:  A293728 A293729 A293730 * A293732 A293733 A293734

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Oct 15 2017

STATUS

approved

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Last modified May 24 15:25 EDT 2019. Contains 323532 sequences. (Running on oeis4.)