A131623 Number of blocks in all partitions of n-set with distinct block sizes.
1, 1, 7, 9, 31, 223, 442, 1529, 6559, 66111, 159952, 742503, 3047656, 19094286, 245173117, 761328969, 3935539271, 20213664703, 117323673136, 897132508439, 15791065424134, 56649181720176, 353387529508691, 1955231849465423
Offset: 1
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..300
Programs
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Maple
A131623 := proc(n) local su,i ; su := add(x^i/(i!+x^i),i=1..n+1) ; for i from 1 to n do su := taylor(su*(1+x^i/i!),x=0,n+1) ; od: n!*coeftayl(su,x=0,n) ; end: seq(A131623(n),n=1..30) ; # R. J. Mathar, Oct 25 2007
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Mathematica
nn=20;p=Product[1+y x^i/i!,{i,1,nn}];Range[0,nn]! CoefficientList[Series[D[p,y]/.y->1,{x,0,nn}],x] (* Geoffrey Critzer, Aug 30 2012 *)
Formula
E.g.f.: Sum(x^n/(n!+x^n),n=1..inf)*Product(1+x^n/n!,n=1..inf).
Extensions
More terms from R. J. Mathar, Oct 25 2007