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A103738 a(n) = n! * (sum of reciprocals of parts in all partitions of n into distinct parts). 2
1, 1, 11, 38, 274, 2844, 21888, 231888, 2580912, 37879200, 459884160, 7372650240, 112624905600, 2002334100480, 37047155846400, 721997863372800, 14458523340441600, 320885263596441600, 7222523219238297600, 172441642330718208000, 4367517061604788224000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..400

FORMULA

E.g.f.: A(x)*B(x), where A(x) = Sum_{k>0} x^k/(k*(1+x^k)) and B(x) = Product_{k>0} (1 + x^k).

MAPLE

gf:=sum(x^k/k/(1+x^k), k=1..50)*product((1+x^k), k=1..50): s:=series(gf, x, 50): for n from 1 to 30 do printf(`%d, `, coeff(s, x, n)*n!) od: # James A. Sellers, Apr 10 2005

# second Maple program:

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

       b(n, i-1)+`if`(i>n, 0, (p-> p+[0, p[1]/i])(b(n-i, i-1)))))

    end:

a:= n-> n!*b(n$2)[2]:

seq(a(n), n=1..30);  # Alois P. Heinz, Sep 11 2014

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, b[n, i - 1] + If[i > n, 0, Function[p, p + {0, p[[1]]/i}][b[n - i, i - 1]]]]]; a[n_] := n!*b[n, n][[2]]; Table[a[n], {n, 1, 30}] (* Jean-Fran├žois Alcover, Jan 10 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A057623.

Sequence in context: A213775 A133258 A288745 * A045801 A162261 A004188

Adjacent sequences:  A103735 A103736 A103737 * A103739 A103740 A103741

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Mar 27 2005

EXTENSIONS

More terms from James A. Sellers, Apr 10 2005

STATUS

approved

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Last modified February 16 08:26 EST 2019. Contains 320159 sequences. (Running on oeis4.)