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A236625
Total number of parts in all overcompositions of n.
3
0, 2, 6, 24, 66, 180, 496, 1272, 3202, 7798, 18980, 45076, 106288, 246956, 568776, 1299184, 2944654, 6630660, 14838606, 33026000, 73126376, 161198136, 353812612, 773645124, 1685548792, 3660364490, 7924414752, 17107225340, 36832846344, 79107019964, 169505684844
OFFSET
0,2
COMMENTS
For the definition of overcomposition see A236002.
The equivalent sequence for overpartitions is A235792.
Row sums of triangle A236628.
LINKS
EXAMPLE
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.
MAPLE
b:= proc(n, i, p) option remember; `if`(n=0, [p!, 0],
`if`(i<1, 0, add((p-> p+[0, p[1]*j])(1/j!*
`if`(j>0, 2, 1)*b(n-i*j, i-1, p+j)), j=0..n/i)))
end:
a:= n-> b(n$2, 0)[2]:
seq(a(n), n=0..35); # Alois P. Heinz, Apr 28 2016
MATHEMATICA
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}]]];
a[n_] := b[n, n, 0][[2]];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Nov 03 2022, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 01 2014
EXTENSIONS
a(6)-a(30) from Alois P. Heinz, Feb 02 2014
STATUS
approved