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A300514 Expansion of e.g.f. exp(Sum_{k>=1} q(k)*x^k/k!), where q(k) = number of partitions of k into distinct parts (A000009). 3
1, 1, 2, 6, 20, 79, 358, 1791, 9854, 58958, 379716, 2617320, 19197327, 149099827, 1221390172, 10515829901, 94865603724, 894302028718, 8788782784778, 89848652800152, 953666248076772, 10491219933196228, 119429574273909421, 1404835599743325765, 17052591331677804136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Exponential transform of A000009.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..550

N. J. A. Sloane, Transforms

Index entries for related partition-counting sequences

FORMULA

E.g.f.: exp(Sum_{k>=1} A000009(k)*x^k/k!).

EXAMPLE

E.g.f.: A(x) = 1 + x/1! + 2*x^2/2! + 6*x^3/3! + 20*x^4/4! + 79*x^5/5! + 358*x^6/6! + 1791*x^7/7! + ...

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-j)*binomial(n-1, j-1)*b(j), j=1..n))

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Mar 07 2018

MATHEMATICA

nmax = 24; CoefficientList[Series[Exp[Sum[PartitionsQ[k] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

a[n_] := a[n] = Sum[PartitionsQ[k] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 24}]

CROSSREFS

Cf. A000009, A293839, A293840, A300511, A300515.

Sequence in context: A081563 A038393 A027221 * A150183 A150184 A150185

Adjacent sequences:  A300511 A300512 A300513 * A300515 A300516 A300517

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 07 2018

STATUS

approved

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Last modified April 6 07:52 EDT 2020. Contains 333267 sequences. (Running on oeis4.)