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 A335980 Expansion of e.g.f. exp(2 * (1 - exp(-x)) + x). 3
 1, 3, 7, 11, 7, -5, 23, 75, -281, -101, 4663, -14229, -41721, 532667, -1464489, -8840053, 103689511, -313202725, -2348557705, 32041266859, -127039882425, -762423051013, 14393151011735, -81523161874741, -236027974047897, 8564406463119387 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) = exp(2) * (-1)^n * Sum_{k>=0} (-2)^k * (k - 1)^n / k!. a(0) = 1; a(n) = a(n-1) + 2 * Sum_{k=0..n-1} (-1)^(n-k-1) * binomial(n-1,k) * a(k). MATHEMATICA nmax = 25; CoefficientList[Series[Exp[2 (1 - Exp[-x]) + x], {x, 0, nmax}], x] Range[0, nmax]! a[0] = 1; a[n_] := a[n] = a[n - 1] + 2 Sum[(-1)^(n - k - 1) Binomial[n - 1, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 25}] PROG (PARI)  my(N=33, x='x+O('x^N)); Vec(serlaplace(exp(2 * (1 - exp(-x)) + x))) \\ Joerg Arndt, Jul 04 2020 CROSSREFS Cf. A001861, A035009, A109747, A213170, A335868, A335981, A335982. Sequence in context: A125255 A125254 A093931 * A153788 A167486 A260408 Adjacent sequences:  A335977 A335978 A335979 * A335981 A335982 A335983 KEYWORD sign AUTHOR Ilya Gutkovskiy, Jul 03 2020 STATUS approved

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Last modified June 22 11:17 EDT 2021. Contains 345375 sequences. (Running on oeis4.)