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 A351777 Expansion of e.g.f. 1/(1 + 2*x*exp(x)). 2
 1, -2, 4, -6, -8, 150, -972, 3682, 6256, -289746, 3300460, -21071622, -27876312, 3156947014, -53217341660, 494232431250, 175171749088, -113735274256290, 2613309376750812, -32653995355358678, 36013529538641560, 10227377502146048118, -305630239215263764076 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..22. FORMULA a(n) = n! * Sum_{k=0..n} (-2)^(n-k) * (n-k)^k/k!. a(0) = 1 and a(n) = -2 * n * Sum_{k=0..n-1} binomial(n-1,k) * a(k) for n > 0. MATHEMATICA With[{nn=30}, CoefficientList[Series[1/(1+2x Exp[x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Feb 06 2024 *) PROG (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1+2*x*exp(x)))) (PARI) a(n) = n!*sum(k=0, n, (-2)^(n-k)*(n-k)^k/k!); (PARI) a(n) = if(n==0, 1, -2*n*sum(k=0, n-1, binomial(n-1, k)*a(k))); CROSSREFS Column k=2 of A351776. Cf. A351762. Sequence in context: A115336 A119666 A087302 * A030149 A083146 A306091 Adjacent sequences: A351774 A351775 A351776 * A351778 A351779 A351780 KEYWORD sign AUTHOR Seiichi Manyama, Feb 19 2022 STATUS approved

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Last modified April 15 00:51 EDT 2024. Contains 371667 sequences. (Running on oeis4.)