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A305850
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Weigh transform of the Bell numbers (A000110).
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4
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1, 1, 2, 7, 21, 78, 305, 1304, 6007, 29854, 159012, 904986, 5479078, 35150263, 238033523, 1695554145, 12663533586, 98881246850, 805128085616, 6820302066048, 59983405937707, 546690232627480, 5154757226832625, 50208266917662433, 504482106565647708
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listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: Product_{k>=1} (1+x^k)^Bell(k).
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MAPLE
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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(g(i), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..30);
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MATHEMATICA
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g[n_] := g[n] = If[n == 0, 1,
Sum[Binomial[n - 1, j - 1]*g[n - j], {j, 1, n}]];
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0,
Sum[Binomial[g[i], j]*b[n - i*j, i - 1], {j, 0, n/i}]]];
a[n_] := b[n, n];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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