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A191459
G.f.: 1 = Sum_{n>=0} a(n) * x^n*(1 - (n+1)*x)^(n+1).
0
1, 1, 4, 32, 404, 7136, 164088, 4683680, 160473988, 6437653568, 296657482888, 15467576203136, 901391710293832, 58122426582341120, 4111838048797360624, 316858691136196764672, 26432968974665127895908, 2374343115004631725352960
OFFSET
0,3
COMMENTS
Compare to a g.f. for A000272:
1 = Sum_{n>=0} (n+1)^(n-1) * x^n/(1 + (n+1)*x)^(n+1).
FORMULA
a(n) = Sum_{k=1..[(n+1)/2]} -(-1)^k * C(n+1-k,k) * (n+1-k)^k * a(n-k).
EXAMPLE
G.f.: 1 = (1-x) + x*(1-2*x)^2 + 4*x^2*(1-3*x)^3 + 32*x^3*(1-4*x)^4 + 404*x^4*(1-5*x)^5 + 7136*x^5*(1-6*x)^6 +...
Compare to a g.f. for A000272:
1 = 1/(1+x) + x/(1+2*x)^2 + 3*x^2/(1+3*x)^3 + 4^2*x^3/(1+4*x)^4 + 5^3*x^4/(1+5*x)^5 + 6^4*x^5/(1+6*x)^6 +...
PROG
(PARI) {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-(k+1)*x+x*O(x^n))^(k+1)), n)}
(PARI) {a(n)=if(n==0, 1, -sum(k=1, (n+1)\2, (-1)^k*binomial(n+1-k, k)*a(n-k)*(n+1-k)^k))}
CROSSREFS
Sequence in context: A243468 A317677 A365603 * A184359 A350465 A229548
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 02 2011
STATUS
approved