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A306009 Inverse Weigh transform of A000085. 2
1, 2, 2, 7, 14, 43, 130, 446, 1544, 5773, 22170, 89356, 370198, 1591379, 7020014, 31922981, 148679262, 710828036, 3474337098, 17379964444, 88739068866, 462670294023, 2458638559154, 13317850411827, 73432568553848, 412120738922369, 2351720323257872 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Product_{k>=1} (1+x^k)^a(k) = Sum_{n>=0} A000085(n) * x^n.
MAPLE
g:= proc(n) option remember;
`if`(n<2, 1, g(n-1)+(n-1)*g(n-2))
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 < 2, 1, g[n - 1] + (n - 1)*g[n - 2]];
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];
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Oct 27 2021, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A187306 A061274 A061575 * A290646 A133602 A137249
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 16 2018
STATUS
approved

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Last modified April 23 11:25 EDT 2024. Contains 371913 sequences. (Running on oeis4.)