A103738 a(n) = n! * (sum of reciprocals of parts in all partitions of n into distinct parts).

1, 1, 11, 38, 274, 2844, 21888, 231888, 2580912, 37879200, 459884160, 7372650240, 112624905600, 2002334100480, 37047155846400, 721997863372800, 14458523340441600, 320885263596441600, 7222523219238297600, 172441642330718208000, 4367517061604788224000

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-François Alcover, Jan 10 2016, after Alois P. Heinz *)

Crossrefs

Cf. A057623.

Sequence in context: A213775 A133258 A288745 * A348487 A045801 A162261

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