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A236625 Total number of parts in all overcompositions of n.

%I A236625 #21 Nov 03 2022 08:42:59
%S A236625 0,2,6,24,66,180,496,1272,3202,7798,18980,45076,106288,246956,568776,
%T A236625 1299184,2944654,6630660,14838606,33026000,73126376,161198136,
%U A236625 353812612,773645124,1685548792,3660364490,7924414752,17107225340,36832846344,79107019964,169505684844
%N A236625 Total number of parts in all overcompositions of n.
%C A236625 For the definition of overcomposition see A236002.
%C A236625 The equivalent sequence for overpartitions is A235792.
%C A236625 Row sums of triangle A236628.
%H A236625 Alois P. Heinz, <a href="/A236625/b236625.txt">Table of n, a(n) for n = 0..1000</a>
%e A236625 For n = 3 the 12 overcompositions of 3 are [3], [3'], [1, 2], [1', 2], [1, 2'], [1', 2'], [2, 1], [2', 1], [2, 1'], [2', 1'], [1, 1, 1], [1', 1, 1]. There are 24 parts, so a(3) = 24.
%p A236625 b:= proc(n, i, p) option remember; `if`(n=0, [p!, 0],
%p A236625       `if`(i<1, 0, add((p-> p+[0, p[1]*j])(1/j!*
%p A236625       `if`(j>0, 2, 1)*b(n-i*j, i-1, p+j)), j=0..n/i)))
%p A236625     end:
%p A236625 a:= n-> b(n$2, 0)[2]:
%p A236625 seq(a(n), n=0..35);  # _Alois P. Heinz_, Apr 28 2016
%t A236625 b[n_, i_, p_] := b[n, i, p] = If[n == 0, {p!, 0}, If[i < 1, {0, 0}, Sum[# + {0, #[[1]]*j}&[1/j!*If[j > 0, 2, 1]*b[n - i*j, i - 1, p + j]], {j, 0, n/i}]]];
%t A236625 a[n_] := b[n, n, 0][[2]];
%t A236625 Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Nov 03 2022, after _Alois P. Heinz_ *)
%Y A236625 Cf. A001792, A006128, A235999, A236002, A235792, A236626, A236628, A236633.
%K A236625 nonn
%O A236625 0,2
%A A236625 _Omar E. Pol_, Feb 01 2014
%E A236625 a(6)-a(30) from _Alois P. Heinz_, Feb 02 2014