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A305846 Inverse Weigh transform of the Bell numbers (A000110). 4
1, 2, 3, 11, 34, 138, 610, 2976, 15612, 87905, 526274, 3334988, 22270254, 156173299, 1146640394, 8791427525, 70227355786, 583283756678, 5027823752930, 44903579714037, 414877600876638, 3959945233249877, 38996757506464858, 395749369601741015, 4134132167178705732 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..576

FORMULA

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

MAPLE

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

      add(binomial(n-1, j-1)*g(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);

CROSSREFS

Cf. A000110, A085686, A168246, A305850, A305853.

Sequence in context: A300771 A296005 A159458 * A057838 A219497 A006497

Adjacent sequences:  A305843 A305844 A305845 * A305847 A305848 A305849

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 11 2018

STATUS

approved

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Last modified April 19 09:12 EDT 2021. Contains 343110 sequences. (Running on oeis4.)