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 A187741 G.f.: Sum_{n>=0} (1 + n*x)^n * x^n / (1 + x + n*x^2)^n. 7
 1, 1, 1, 2, 3, 6, 12, 24, 60, 120, 360, 720, 2520, 5040, 20160, 40320, 181440, 362880, 1814400, 3628800, 19958400, 39916800, 239500800, 479001600, 3113510400, 6227020800, 43589145600, 87178291200, 653837184000, 1307674368000, 10461394944000, 20922789888000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS FORMULA G.f.: 1/2 + (1+2*x) * Sum_{n>=0} (n+1)!*x^(2*n)/2. a(2*n) = (n+1)!/2,  a(2*n-1) = n!,  for n>0 with a(0)=1. EXAMPLE G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 6*x^5 + 12*x^6 + 24*x^7 + 60*x^8 +... where A(x) = 1 + (1+x)*x/(1+x+x^2) + (1+2*x)^2*x^2/(1+x+2*x^2)^2 + (1+3*x)^3*x^3/(1+x+3*x^2)^3 + (1+4*x)^4*x^4/(1+x+4*x^2)^4 + (1+5*x)^5*x^5/(1+x+5*x^2)^5 +... PROG (PARI) {a(n)=polcoeff( sum(m=0, n, (x+m*x^2)^m / (1 + x+m*x^2 +x*O(x^n))^m), n)} for(n=0, 40, print1(a(n), ", ")) (PARI) {a(n)=if(n==0, 1, if(n%2==0, ((n+2)/2)!/2, ((n+1)/2)! ))} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A187742, A187735, A208236, A204064. Sequence in context: A119559 A329675 A045761 * A216632 A077903 A038086 Adjacent sequences:  A187738 A187739 A187740 * A187742 A187743 A187744 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 03 2013 STATUS approved

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Last modified August 13 19:30 EDT 2020. Contains 336451 sequences. (Running on oeis4.)