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 A221988 G.f.: Sum_{n>=0} n! * (2*x)^n * Product_{k=1..n} (1 + k*x)/(1 + 2*k*x + 2*k^2*x^2). 1
 1, 2, 6, 24, 116, 664, 4392, 32928, 276016, 2557856, 25965408, 286538112, 3415359296, 43727878528, 598510015104, 8720853182976, 134778021389056, 2202055694727680, 37923940767905280, 686639853639505920, 13038833241899856896, 259119925532534413312 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS EXAMPLE G.f.: A(x) = 1 + 2*x + 6*x^2 + 24*x^3 + 116*x^4 + 664*x^5 + 4392*x^6 +... where A(x) = 1 + (2*x)*(1+x)/(1+2*x+2*x^2) + 2!*(2*x)^2*(1+x)*(1+2*x)/((1+2*x+2*x^2)*(1+4*x+8*x^2)) + 3!*(2*x)^3*(1+x)*(1+2*x)*(1+3*x)/((1+2*x+2*x^2)*(1+4*x+8*x^2)*(1+6*x+18*x^2)) + 4!*(2*x)^4*(1+x)*(1+2*x)*(1+3*x)*(1+4*x)/((1+2*x+2*x^2)*(1+4*x+8*x^2)*(1+6*x+18*x^2)*(1+8*x+32*x^2)) +... PROG (PARI) {a(n)=polcoeff( sum(m=0, n, m!*(2*x)^m*prod(k=1, m, (1+k*x)/(1+2*k*x+2*k^2*x^2 +x*O(x^n))) ), n)} for(n=0, 25, print1(a(n), ", ")) CROSSREFS Cf. A221987, A208237, A136127, A221973. Sequence in context: A007405 A324130 A324131 * A329788 A177518 A319027 Adjacent sequences:  A221985 A221986 A221987 * A221989 A221990 A221991 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 02 2013 STATUS approved

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Last modified September 26 21:46 EDT 2020. Contains 337377 sequences. (Running on oeis4.)