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A324237 Expansion of e.g.f. 1 / (1 - Sum_{k>=1} q(k)*x^k/k!), where q(k) = number of partitions of k into distinct parts (A000009). 2
1, 1, 3, 14, 84, 633, 5730, 60485, 729710, 9904064, 149358998, 2477662364, 44837516675, 879028693860, 18558771941586, 419815668642109, 10129704474860688, 259695154154923814, 7049438079064414206, 201988316828399901634, 6092203404985463075656 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..419

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * q(k) * a(n-k).

a(n) ~ c * d^n * n!, where d = 1.5080583621492799630678624980320180394686208919872154400104169910221003637... and c = 0.67652958824662835367141799671720225317465169475061770258661897351... - Vaclav Kotesovec, Sep 03 2019

MAPLE

b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(

     `if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)

    end:

a:= proc(n) option remember; `if`(n=0, 1, add(

      a(n-k)*binomial(n, k)*b(k), k=1..n))

    end:

seq(a(n), n=0..20);  # Alois P. Heinz, Sep 02 2019

MATHEMATICA

nmax = 21; CoefficientList[Series[1/(1 - Sum[PartitionsQ[k] x^k/k!, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] PartitionsQ[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]

CROSSREFS

Cf. A000009, A266232, A300514, A304969, A324236.

Sequence in context: A220911 A088717 A111538 * A230218 A301934 A160881

Adjacent sequences:  A324234 A324235 A324236 * A324238 A324239 A324240

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 02 2019

STATUS

approved

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Last modified October 28 11:19 EDT 2021. Contains 348329 sequences. (Running on oeis4.)