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 A295182 a(n) = n! * [x^n] exp(-n*x)/(1 - x)^n. 3
 1, 0, 2, 6, 72, 620, 8640, 122346, 2156672, 41367672, 905126400, 21646532270, 570077595648, 16268377195044, 502096929431552, 16629319748711250, 588938142209310720, 22196966267762213744, 887352465220427317248, 37496112562144553167062, 1670071417348195942400000, 78195398849926292810318940 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The n-th term of the n-fold exponential convolution of A000166 with themselves. LINKS Robert Israel, Table of n, a(n) for n = 0..396 N. J. A. Sloane, Transforms FORMULA a(n) = A295181(n,n). a(n) ~ phi^(3*n - 1/2) * n^n / (5^(1/4) * exp(n*(1 + 1/phi))), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Nov 16 2017 MAPLE S:= series((exp(-x)/(1-x))^n, x, 30): seq(n!*coeff(S, x, n), n=0..29); # Robert Israel, Nov 16 2017 MATHEMATICA Table[n! SeriesCoefficient[Exp[-n x]/(1 - x)^n, {x, 0, n}], {n, 0, 21}] CROSSREFS Main diagonal of A295181. Cf. A000166, A000407, A001813, A087981, A137775, A295183. Sequence in context: A329965 A171582 A152885 * A052613 A156493 A218891 Adjacent sequences:  A295179 A295180 A295181 * A295183 A295184 A295185 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Nov 16 2017 STATUS approved

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Last modified December 13 01:23 EST 2019. Contains 329963 sequences. (Running on oeis4.)