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A131623 Number of blocks in all partitions of n-set with distinct block sizes. 2

%I

%S 1,1,7,9,31,223,442,1529,6559,66111,159952,742503,3047656,19094286,

%T 245173117,761328969,3935539271,20213664703,117323673136,897132508439,

%U 15791065424134,56649181720176,353387529508691,1955231849465423

%N Number of blocks in all partitions of n-set with distinct block sizes.

%H Alois P. Heinz, <a href="/A131623/b131623.txt">Table of n, a(n) for n = 1..300</a>

%F E.g.f.: Sum(x^n/(n!+x^n),n=1..inf)*Product(1+x^n/n!,n=1..inf).

%p 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

%t 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 *)

%Y Cf. A044048, A007837.

%K easy,nonn

%O 1,3

%A _Vladeta Jovovic_, Sep 02 2007

%E More terms from _R. J. Mathar_, Oct 25 2007

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Last modified March 29 13:26 EDT 2020. Contains 333107 sequences. (Running on oeis4.)