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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

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-Fran├žois Alcover, May 21 2018, translated from Maple *)

CROSSREFS

Cf. A114638 (the same for partitions).

Sequence in context: A091884 A255257 A306769 * A048156 A070431 A070511

Adjacent sequences:  A243146 A243147 A243148 * A243150 A243151 A243152

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 30 2014

STATUS

approved

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)