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A097148 Total sum of maximum block sizes in all partitions of n-set. 5

%I

%S 1,3,10,35,136,577,2682,13435,72310,414761,2524666,16239115,109976478,

%T 781672543,5814797281,45155050875,365223239372,3070422740989,

%U 26780417126048,241927307839731,2260138776632752,21805163768404127

%N Total sum of maximum block sizes in all partitions of n-set.

%C Let M be the infinite lower triangular matrix given by A080510 and v the column vector [1,2,3,...] then M*v=A097148 (this sequence, as column vector). - _Gary W. Adamson_, Feb 24 2011

%H Alois P. Heinz, <a href="/A097148/b097148.txt">Table of n, a(n) for n = 1..576</a>

%F E.g.f.: Sum_{k>=0} (exp(exp(x)-1)-exp(Sum_{j=1..k} x^j/j!)).

%p b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,

%p add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(

%p combinat[multinomial](n, i$j, n-i*j)/j!*

%p b(n-i*j, min(n-i*j, i-1), max(0, t-j))), j=0..n/i)))

%p end:

%p a:= n-> b(n$2, 1)[2]:

%p seq(a(n), n=1..23); # _Alois P. Heinz_, Mar 02 2020

%p # second Maple program:

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p add(b(n-i*j, i-1)*n!/i!^j/(n-i*j)!/j!, j=0..n/i)))

%p end:

%p a:= n-> add((b(n, k)-b(n, k-1))*k, k=1..n):

%p seq(a(n), n=1..23); # _Alois P. Heinz_, Mar 02 2020

%t Drop[ Range[0, 22]! CoefficientList[ Series[ Sum[E^(E^x - 1) - E^Sum[x^j/j!, {j, 1, k}], {k, 0, 22}], {x, 0, 22}], x], 1] (* _Robert G. Wilson v_, Aug 05 2004 *)

%Y Cf. A028417, A028418, A046746, A006128, A097145-A097147.

%Y Cf. A080510.

%Y Column k=1 of A319375.

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, Jul 27 2004

%E More terms from _Robert G. Wilson v_, Aug 05 2004

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Last modified April 16 21:58 EDT 2021. Contains 343051 sequences. (Running on oeis4.)