A353290 a(n) = Sum_{k=0..floor(n/2)} (n-k)^(n-2*k) * |Stirling1(n-k,k)|.
1, 0, 1, 2, 19, 393, 15177, 939394, 85063260, 10599342278, 1739073390797, 363404567436467, 94224446795779884, 29683590039199285223, 11167286542016941966714, 4945143125245884296040780, 2546112368234517215955646341, 1508197687055444623135714912377
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, k*j+x))) -
PARI
a(n) = sum(k=0, n\2, (n-k)^(n-2*k)*abs(stirling(n-k, k, 1)));
Formula
G.f.: Sum_{k>=0} x^k * Product_{j=0..k-1} (k * j + x).