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A318179 Expansion of e.g.f. exp((1 - exp(-4*x))/4). 7
1, 1, -3, 5, 25, -343, 2133, -3603, -112975, 1938897, -18008275, 55198805, 1753746377, -45801271943, 649021707397, -4682002329795, -50792700319903, 2692784088681889, -59182401177647011, 801759226622986917, -2169423359710146183, -263145142263538606519, 9869607872225170545333 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

Eric Weisstein's World of Mathematics, Bell Polynomial

FORMULA

a(n) = Sum_{k=0..n} (-4)^(n-k)*Stirling2(n,k).

a(0) = 1; a(n) = Sum_{k=1..n} (-4)^(k-1)*binomial(n-1,k-1)*a(n-k).

a(n) = (-4)^n*BellPolynomial_n(-1/4). - Peter Luschny, Aug 20 2018

MAPLE

seq(n!*coeff(series(exp((1-exp(-4*x))/4), x=0, 23), x, n), n=0..22); # Paolo P. Lava, Jan 09 2019

MATHEMATICA

nmax = 22; CoefficientList[Series[Exp[(1 - Exp[-4 x])/4], {x, 0, nmax}], x] Range[0, nmax]!

Table[Sum[(-4)^(n - k) StirlingS2[n, k], {k, 0, n}], {n, 0, 22}]

a[n_] := a[n] = Sum[(-4)^(k - 1) Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 22}]

Table[(-4)^n BellB[n, -1/4], {n, 0, 22}] (* Peter Luschny, Aug 20 2018 *)

CROSSREFS

Cf. A004213, A007696, A009235, A014182, A317996, A318180, A318181.

Sequence in context: A119882 A276968 A074701 * A327468 A140127 A226318

Adjacent sequences:  A318176 A318177 A318178 * A318180 A318181 A318182

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Aug 20 2018

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)