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A243149
Number of compositions of n such that the sum of the parts counted without multiplicities is equal to the sum of all multiplicities.
2
1, 1, 0, 0, 4, 3, 4, 0, 11, 31, 70, 177, 242, 382, 482, 874, 1655, 4440, 10696, 24390, 49867, 95850, 172980, 289229, 492233, 811753, 1468084, 2813206, 5929361, 12780690, 27858421, 59275097, 122326098, 243179349, 467856049, 873044584, 1588187110, 2842593612
OFFSET
0,5
LINKS
EXAMPLE
a(8) = 11: [1,1,3,3], [1,3,1,3], [1,3,3,1], [3,1,1,3], [3,1,3,1], [3,3,1,1], [1,1,1,1,4], [1,1,1,4,1], [1,1,4,1,1], [1,4,1,1,1], [4,1,1,1,1].
MAPLE
b:= proc(n, i, p) option remember; `if`(n=0, p!,
`if`(i<1, 0, expand(add(x^`if`(j=0, 0, i-j)*
b(n-i*j, i-1, p+j)/j!, j=0..n/i))))
end:
a:= n-> coeff(b(n$2, 0), x, 0):
seq(a(n), n=0..50);
MATHEMATICA
b[n_, i_, p_] := b[n, i, p] = If[n == 0, p!, If[i < 1, 0, Expand[Sum[x^If[j == 0, 0, i - j]*b[n - i*j, i - 1, p + j]/j!, {j, 0, n/i}]]]];
a[n_] := Coefficient[b[n, n, 0], x, 0];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, May 21 2018, translated from Maple *)
CROSSREFS
Cf. A114638 (the same for partitions).
Sequence in context: A306769 A336031 A329982 * A048156 A070431 A070511
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 30 2014
STATUS
approved