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A305853 Inverse Weigh transform of the Fubini numbers (ordered Bell numbers, A000670). 3
1, 3, 10, 62, 446, 3975, 41098, 484152, 6390488, 93419965, 1498268466, 26159940522, 494036061550, 10035451747919, 218207845446062, 5057251219752612, 124462048466812950, 3241773988594489244, 89093816361187396674, 2576652694087236419386, 78224564280680539732266 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..424

FORMULA

Product_{k>=1} (1+x^k)^a(k) = Sum_{n>=0} A000670(n) * x^n.

a(n) ~ n! / (2 * log(2)^(n+1)). - Vaclav Kotesovec, Sep 10 2019

MAPLE

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

      add(g(n-j)*binomial(n, j), j=1..n))

    end:

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))

    end:

a:= proc(n) option remember; g(n)-b(n, n-1) end:

seq(a(n), n=1..30);

MATHEMATICA

g[n_] := g[n] = If[n == 0, 1,

    Sum[g[n - j] Binomial[n, j], {j, 1, n}]];

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0,

    Sum[Binomial[a[i], j] b[n - i j, i - 1], {j, 0, n/i}]]];

a[n_] := a[n] = g[n] - b[n, n - 1];

a /@ Range[1, 30] (* Jean-Fran├žois Alcover, Dec 21 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A000670, A095993, A305846, A305852.

Sequence in context: A034889 A228773 A260969 * A160921 A042705 A041014

Adjacent sequences:  A305850 A305851 A305852 * A305854 A305855 A305856

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 11 2018

STATUS

approved

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Last modified January 22 23:09 EST 2021. Contains 340383 sequences. (Running on oeis4.)