# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a317996 Showing 1-1 of 1 %I A317996 #30 Jul 28 2019 16:53:45 %S A317996 1,1,-2,1,19,-128,379,1549,-32600,261631,-845909,-10713602,237695149, %T A317996 -2513395259,11792378662,151915180429,-4826456213273,70741388773960, %U A317996 -558513179369297,-2833805536521839,200720356696607416,-4256279445015662093,54120395442382043743,-173423789950999240226 %N A317996 Expansion of e.g.f. exp((1 - exp(-3*x))/3). %H A317996 Seiichi Manyama, Table of n, a(n) for n = 0..495 %H A317996 Eric Weisstein's World of Mathematics, Bell Polynomial %F A317996 a(n) = Sum_{k=0..n} (-3)^(n-k)*Stirling2(n,k). %F A317996 a(0) = 1; a(n) = Sum_{k=1..n} (-3)^(k-1)*binomial(n-1,k-1)*a(n-k). %F A317996 a(n) = (-3)^n BellPolynomial_n(-1/3). - _Peter Luschny_, Aug 20 2018 %p A317996 a:=series(exp((1 - exp(-3*x))/3), x=0, 24): seq(n!*coeff(a, x, n), n=0..23); # _Paolo P. Lava_, Mar 26 2019 %t A317996 nmax = 23; CoefficientList[Series[Exp[(1 - Exp[-3 x])/3], {x, 0, nmax}], x] Range[0, nmax]! %t A317996 Table[Sum[(-3)^(n - k) StirlingS2[n, k], {k, 0, n}], {n, 0, 23}] %t A317996 a[n_] := a[n] = Sum[(-3)^(k - 1) Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}] %t A317996 Table[(-3)^n BellB[n, -1/3], {n, 0, 23}] (* _Peter Luschny_, Aug 20 2018 *) %Y A317996 Column k=3 of A309386. %Y A317996 Cf. A004212, A007559, A009235, A014182, A318179, A318180, A318181. %K A317996 sign %O A317996 0,3 %A A317996 _Ilya Gutkovskiy_, Aug 20 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE