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 A351762 Expansion of e.g.f. 1/(1 - 2*x*exp(x)). 7
 1, 2, 12, 102, 1160, 16490, 281292, 5598110, 127326096, 3257961426, 92625793940, 2896747456262, 98827517418456, 3652643136982970, 145385563800940764, 6200097935648462190, 282035994269804870432, 13631368700936950044578, 697586352315912913754916 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..18. 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. a(n) ~ n! / ((1 + LambertW(1/2)) * LambertW(1/2)^n). - Vaclav Kotesovec, Feb 19 2022 PROG (PARI) my(N=20, 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 A351761. Cf. A000629, A351777. Sequence in context: A113557 A245266 A123897 * A302357 A052693 A050621 Adjacent sequences: A351759 A351760 A351761 * A351763 A351764 A351765 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 18 2022 STATUS approved

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Last modified May 26 18:00 EDT 2024. Contains 372840 sequences. (Running on oeis4.)