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 A307066 a(n) = exp(-1) * Sum_{k>=0} (n*k + 1)^n/k!. 3
 1, 2, 13, 199, 5329, 216151, 12211597, 909102342, 85761187393, 9957171535975, 1390946372509101, 229587693339867567, 44117901231194922193, 9748599124579281064294, 2451233017637221706477037, 695088863051920283838281851, 220558203335628758134165860609 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) = n! * [x^n] exp(exp(n*x) + x - 1). a(n) = Sum_{k=0..n} binomial(n,k) * n^k * Bell(k). MATHEMATICA Table[Exp[-1] Sum[(n k + 1)^n/k!, {k, 0, Infinity}], {n, 0, 16}] Table[n! SeriesCoefficient[Exp[Exp[n x] + x - 1], {x, 0, n}], {n, 0, 16}] Join[{1}, Table[Sum[Binomial[n, k] n^k BellB[k], {k, 0, n}], {n, 1, 16}]] CROSSREFS Cf. A000110, A126390, A134980, A284859, A285064, A292914, A307080. Sequence in context: A049512 A003507 A338979 * A003085 A053598 A193550 Adjacent sequences:  A307063 A307064 A307065 * A307067 A307068 A307069 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jun 24 2019 STATUS approved

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Last modified September 19 03:31 EDT 2021. Contains 347550 sequences. (Running on oeis4.)