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

1, 3, 10, 35, 136, 577, 2682, 13435, 72310, 414761, 2524666, 16239115, 109976478, 781672543, 5814797281, 45155050875, 365223239372, 3070422740989, 26780417126048, 241927307839731, 2260138776632752, 21805163768404127, 216970086170175575, 2224040977932468379

Offset

1,2

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..576

Formula

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

Maple

b:= proc(n, m) option remember; `if`(n=0, m, add(
      b(n-j, max(j, m))*binomial(n-1, j-1), j=1..n))
    end:
a:= n-> b(n, 0):
seq(a(n), n=1..24);  # Alois P. Heinz, Mar 02 2020, revised May 08 2024

Mathematica

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 *)

Crossrefs

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

Keyword

easy,nonn

Author

Vladeta Jovovic, Jul 27 2004

Extensions

More terms from Robert G. Wilson v, Aug 05 2004

Status

approved