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A131623 Number of blocks in all partitions of n-set with distinct block sizes. 2
1, 1, 7, 9, 31, 223, 442, 1529, 6559, 66111, 159952, 742503, 3047656, 19094286, 245173117, 761328969, 3935539271, 20213664703, 117323673136, 897132508439, 15791065424134, 56649181720176, 353387529508691, 1955231849465423 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 27 09:24 EST 2020. Contains 332301 sequences. (Running on oeis4.)