A089005 Number of partitions of n-set with at least one even block.

0, 1, 3, 10, 40, 166, 749, 3683, 19275, 107806, 640970, 4024912, 26653653, 185401581, 1350624721, 10282222002, 81592209580, 673535269054, 5773214891137, 51291776763863, 471617190143567, 4481375500319334, 43947651280912186, 444258975094335440

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..500

Formula

E.g.f.: exp(sinh(x))*(exp(cosh(x)-1)-1).

Maple

with(combinat):
b:= proc(n, i, t) option remember; `if`(n=0, t, `if`(i<1, 0,
       add(multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1,
       max(t, `if`(j=0, 0, 1-irem(i, 2)))), j=0..n/i)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=1..30);

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, t_] := b[n, i, t] = If[n == 0, t, If[i<1, 0, Sum[multinomial[n, {n - i j} ~Join~ Table[i, {j}]]/j! b[n - i j, i - 1, Max[t, If[j == 0, 0, 1 - Mod[i, 2]]]], {j, 0, n/i}]]];
a[n_] := b[n, n, 0];
Array[a, 30] (* Jean-François Alcover, Nov 18 2020, after Maple *)

Prog

(PARI) my(x='x+O('x^30)); concat(0, Vec(serlaplace(exp(sinh(x))*(exp(cosh(x)-1)-1))))

Crossrefs

Cf. A000110, A005046, A003724, A059838, A047967.

Sequence in context: A149055 A254535 A093639 * A287887 A088300 A151074

Adjacent sequences: A089002 A089003 A089004 * A089006 A089007 A089008

Keyword

nonn

Author

Vladeta Jovovic, Nov 02 2003

Status

approved