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A097148
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Total sum of maximum block sizes in all partitions of n-set.
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5
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1, 3, 10, 35, 136, 577, 2682, 13435, 72310, 414761, 2524666, 16239115, 109976478, 781672543, 5814797281, 45155050875, 365223239372, 3070422740989, 26780417126048, 241927307839731, 2260138776632752, 21805163768404127
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..576
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FORMULA
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E.g.f.: Sum_{k>=0} (exp(exp(x)-1)-exp(Sum_{j=1..k} x^j/j!)).
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MAPLE
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b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(
combinat[multinomial](n, i$j, n-i*j)/j!*
b(n-i*j, min(n-i*j, i-1), max(0, t-j))), j=0..n/i)))
end:
a:= n-> b(n$2, 1)[2]:
seq(a(n), n=1..23); # Alois P. Heinz, Mar 02 2020
# second Maple program:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1)*n!/i!^j/(n-i*j)!/j!, j=0..n/i)))
end:
a:= n-> add((b(n, k)-b(n, k-1))*k, k=1..n):
seq(a(n), n=1..23); # Alois P. Heinz, Mar 02 2020
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A028417, A028418, A046746, A006128, A097145-A097147.
Cf. A080510.
Column k=1 of A319375.
Sequence in context: A008984 A151048 A149038 * A149039 A151477 A184175
Adjacent sequences: A097145 A097146 A097147 * A097149 A097150 A097151
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic, Jul 27 2004
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EXTENSIONS
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More terms from Robert G. Wilson v, Aug 05 2004
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STATUS
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approved
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