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

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..300

Formula

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

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

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 *)

Crossrefs

Cf. A044048, A007837.

Sequence in context: A200180 A147248 A147186 * A032011 A272434 A272433

Adjacent sequences: A131620 A131621 A131622 * A131624 A131625 A131626

Keyword

easy,nonn

Author

Vladeta Jovovic, Sep 02 2007

Extensions

More terms from R. J. Mathar, Oct 25 2007

Status

approved