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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 (list; graph; refs; listen; history; text; internal format)
 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). LINKS 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: A317403 A243468 A317677 * A184359 A229548 A005172 Adjacent sequences:  A191456 A191457 A191458 * A191460 A191461 A191462 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 02 2011 STATUS approved

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Last modified August 1 07:45 EDT 2021. Contains 346384 sequences. (Running on oeis4.)