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%I #30 May 08 2024 17:57:20
%S 1,3,10,35,136,577,2682,13435,72310,414761,2524666,16239115,109976478,
%T 781672543,5814797281,45155050875,365223239372,3070422740989,
%U 26780417126048,241927307839731,2260138776632752,21805163768404127,216970086170175575,2224040977932468379
%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, m) option remember; `if`(n=0, m, add(
%p b(n-j, max(j, m))*binomial(n-1, j-1), j=1..n))
%p end:
%p a:= n-> b(n, 0):
%p seq(a(n), n=1..24); # _Alois P. Heinz_, Mar 02 2020, revised May 08 2024
%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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