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A051529 INVERT transform of A000081 = [1, 1, 1, 2, 4, 9, 20, 48, 115, 286,...]. 1

%I

%S 1,2,4,9,21,51,126,318,812,2100,5482,14438,38303,102302,274824,742210,

%T 2013941,5488239,15014376,41221775,113542455,313681756,868994723,

%U 2413526848,6719132105,18746838609,52412080624,146812972155,411977724704,1158006098132

%N INVERT transform of A000081 = [1, 1, 1, 2, 4, 9, 20, 48, 115, 286,...].

%H Alois P. Heinz, <a href="/A051529/b051529.txt">Table of n, a(n) for n = 0..650</a>

%p with(numtheory): b:= proc(n) option remember; local d, j; `if`(n<=1, 1, (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/ (n-1)) end: a:= proc(n) option remember; local i; `if`(n<1, 1, add(a(n-i) *b(i-1), i=1..n+1)) end: seq(a(n), n=0..30); # _Alois P. Heinz_, Apr 01 2009

%t b[n_] := b[n] = If[n <= 1, 1, (Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n - j], {j, 1, n - 1}])/ (n - 1)];

%t a[n_] := a[n] = If[n < 1, 1, Sum[a[n - i]*b[i - 1], {i, 1, n + 1}]];

%t a /@ Range[0, 30] (* _Jean-Fran├žois Alcover_, Mar 01 2021, after _Alois P. Heinz_ *)

%Y Cf. A000081, A000107.

%K nonn

%O 0,2

%A _N. J. A. Sloane_

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Last modified May 6 03:25 EDT 2021. Contains 343580 sequences. (Running on oeis4.)