A141319 INVERTi transform of A141318.
2, 3, 8, 46, 252, 1558, 9800, 64115, 428546, 2921527, 20220128, 141746372, 1004278856, 7180301580, 51739691584, 375370204876, 2739615168344, 20100885190508, 148179065429664, 1096966770610372, 8151826588836472, 60787793832205004, 454719634089674432
Offset: 1
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..1000
- J.-C. Novelli and J.-Y. Thibon, Free quasi-symmetric functions and descent algebras for wreath products and noncommutative multi-symmetric functions, arXiv:0806.3682 [math.CO], 2008.
Programs
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Maple
with(numtheory): b:= proc(n) option remember; `if`(n=0, 1, add(add((2^d)*binomial(2*d-2,d-1), d=divisors(j)) *b(n-j), j=1..n)/n) end: a:= proc(n) option remember; `if`(n<1, -1, -add(a(n-i) *b(i), i=1..n)) end: seq(a(n), n=1..30); # Alois P. Heinz, Jan 27 2012 -
Mathematica
b[n_] := b[n] = If[n==0, 1, Sum[Sum[2^d*Binomial[2*d-2, d-1], {d, Divisors[ j]}]*b[n-j], {j, 1, n}]/n]; a[n_] := a[n] = If[n<1, -1, -Sum[a[n-i]* b[i], {i, 1, n}]]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Feb 24 2016, after Alois P. Heinz *)
Comments