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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 Alois P. Heinz, Table of n, a(n) for n = 1..800 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 Cf. A000085, A293114. Sequence in context: A187306 A061274 A061575 * A290646 A133602 A137249 Adjacent sequences: A306006 A306007 A306008 * A306010 A306011 A306012 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.)