A353289 a(n) = Sum_{k=0..floor(n/2)} (n-k)^k * |Stirling1(n-k,k)|.
1, 0, 1, 2, 10, 51, 323, 2354, 19535, 181606, 1869549, 21110063, 259400501, 3445913273, 49207968328, 751698726580, 12231484211240, 211208935989003, 3857425360784596, 74292198980174828, 1504832580013205275, 31980327844846620785, 711498612995378484414
Offset: 0
Keywords
Programs
-
PARI
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, j+k*x))) -
PARI
a(n) = sum(k=0, n\2, (n-k)^k*abs(stirling(n-k, k, 1)));
Formula
G.f.: Sum_{k>=0} x^k * Product_{j=0..k-1} (j + k * x).