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A091356 Number of planar partitions of n with exactly 2 rows.

%I A091356 #12 Oct 28 2020 10:22:53
%S A091356 1,2,5,9,18,30,53,85,139,215,336,504,760,1115,1635,2351,3375,4770,
%T A091356 6725,9368,13006,17885,24510,33319,45139,60743,81457,108610,144334,
%U A091356 190844,251542,330082,431825,562710,731154,946644,1222305,1573155,2019471
%N A091356 Number of planar partitions of n with exactly 2 rows.
%H A091356 Alois P. Heinz, <a href="/A091356/b091356.txt">Table of n, a(n) for n = 2..10000</a>
%F A091356 a(n) = A000990(n) - A000041(n).
%p A091356 b:= proc(n, k) option remember; `if`(n=0, 1, add(add(min(d, k)
%p A091356      *d, d=numtheory[divisors](j))*b(n-j, k), j=1..n)/n)
%p A091356     end:
%p A091356 a:= n-> b(n, 2)-b(n, 1):
%p A091356 seq(a(n), n=2..50);  # _Alois P. Heinz_, Oct 02 2018
%t A091356 b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[Sum[Min[d, k] d, {d, Divisors[j]}] b[n - j, k], {j, 1, n}]/n];
%t A091356 a[n_] :=  b[n, 2] - b[n, 1];
%t A091356 a /@ Range[2, 50] (* _Jean-François Alcover_, Oct 28 2020, after _Alois P. Heinz_ *)
%Y A091356 Column 2 of A091355.
%Y A091356 Cf. A000219, A091357, A091358, A091359, A091360.
%K A091356 nonn
%O A091356 2,2
%A A091356 _Christian G. Bower_, Jan 02 2004