OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..474
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
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Aug 20 2018
STATUS
approved