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%I #17 Feb 22 2017 10:20:19
%S 1,1,1,2,4,10,26,71,197,564,1639,4833,14406,43374,131652,402525,
%T 1238419,3831520,11912913,37204431,116655147,367100319,1159026041,
%U 3670339794,11655070593,37104257405,118398974620,378627600346,1213247498254,3894924465243
%N Weigh transform of A007561.
%H Alois P. Heinz, <a href="/A035079/b035079.txt">Table of n, a(n) for n = 0..600</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F a(n) ~ c * d^n / n^(3/2), where d = 3.382016466020272807429818743... (same as for A035080), c = 0.2780120087122189647675707... . - _Vaclav Kotesovec_, Sep 12 2014
%p g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p add(binomial(b((i-1)$2), j)*g(n-i*j, i-1), j=0..n/i)))
%p end:
%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p add(binomial(g(i$2), j)*b(n-i*j, i-1), j=0..n/i)))
%p end:
%p a:= n-> g(n, n):
%p seq(a(n), n=0..40); # _Alois P. Heinz_, May 20 2013
%t g[n_, i_] := g[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[b[i-1, i-1], j]* g[n-i*j, i-1], {j, 0, n/i}]]];
%t b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[g[i, i], j]*b[n- i*j, i-1], {j, 0, n/i}]]];
%t a[n_] := g[n, n];
%t Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Feb 22 2017, after _Alois P. Heinz_ *)
%Y Cf. A035080, A035081.
%K nonn
%O 0,4
%A _Christian G. Bower_, Nov 15 1998
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