A277099 - OEIS

%I #9 Sep 30 2016 21:12:43

%S 1,1,1,3,4,6,8,12,18,24,32,45,59,79,104,137,177,229,295,377,477,605,

%T 761,956,1193,1484,1840,2276,2800,3441,4210,5141,6261,7603,9206,11132,

%U 13419,16144,19380,23223,27763,33134,39467,46931,55703,66008,78085,92239,108776,128091,150617

%N Number of partitions of n containing no part i of multiplicity i+1.

%H Alois P. Heinz, <a href="/A277099/b277099.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A276433(n,0).

%F G.f.: g(x) = Product_{i>=1} (1/(1-x^i) - x^(i*(i+1))).

%e a(4) = 4 because we have [1,1,1,1], [1,3], [2,2], and [4]; the partition [1,1,2] does not qualify.

%p g:= product(1/(1-x^i)-x^(i*(i+1)), i = 1 .. 100): gser := series(g, x = 0, 53): seq(coeff(gser, x, n), n = 0 .. 50);

%p # second Maple program:

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

%p       add(`if`(i+1=j, 0, b(n-i*j, i-1)), j=0..n/i)))

%p     end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..60);  # _Alois P. Heinz_, Sep 30 2016

%t nmax = 50; CoefficientList[Series[Product[(1/(1-x^k) - x^(k*(k+1))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 30 2016 *)

%Y Cf. A276427, A276428, A276429, A276433, A276434, A277100, A277101, A277102.

%K nonn

%O 0,4

%A _Emeric Deutsch_, Sep 30 2016