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A274539 E.g.f.: exp(sum(bell(n)*z^n/n, n=1..infinity)). 1
1, 1, 3, 17, 155, 2079, 38629, 951187, 29979753, 1175837345, 56066617331, 3187704802281, 212628685506643, 16413606252207007, 1449425836362499605, 144977415195565990619, 16285937949513614300369, 2039447464767566886933057, 282862729890000953318773603 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
The structure of the n!*P(n) formulas leads to the multinomial coefficients A036039.
Some transform pairs, see the formula section, are: x(n) = A000027(n) and a(n) = A000262(n); x(n) = A000045(n) and a(n) = A244430(n); x(n) = A000079(n) and a(n) = A000165(n); x(n) = A000108(n) and a(n) = A213507(n); x(n) = A000142(n) and a(n) = A158876(n); x(n) = A000203(n) and a(n) = A053529(n).
LINKS
FORMULA
a(n) = n! * P(n), with P(n) = (1/n)*(sum(x(n-k) * P(k), k=0..n-1)), n >=1 and P(0) = 1, with x(n) = A000110(n), the Bell numbers.
E.g.f.: exp(sum(x(n)*z^n/n, n=1..infinity)) with x(n) = A000110(n).
MAPLE
a := proc(n): n!*P(n) end: P := proc(n): if n=0 then 1 else P(n):= expand((1/n)*(add(x(n-k) * P(k), k=0..n-1))) fi; end: with(combinat): x := proc(n): bell(n) end: seq(a(n), n=0..18);
MATHEMATICA
nmax = 20; CoefficientList[Series[E^(Sum[BellB[n]*z^n/n, {n, 1, nmax}]), {z, 0, nmax}], z] * Range[0, nmax]! (* Vaclav Kotesovec, Jun 29 2016 *)
CROSSREFS
Sequence in context: A168441 A001469 A110501 * A356639 A354772 A066211
KEYWORD
nonn
AUTHOR
Johannes W. Meijer, Jun 29 2016
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)