OFFSET
0,6
COMMENTS
Shifts left 3 places under Stirling transform.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..371
Ronald Orozco López, Solution of the Differential Equation y^(k)= e^(a*y), Special Values of Bell Polynomials and (k,a)-Autonomous Coefficients, Universidad de los Andes (Colombia 2021).
FORMULA
E.g.f. A(x) satisfies A(x) = 1 + x + x^2/2 + Integral( Integral( Integral A(exp(x) - 1) dx) dx) dx.
MAPLE
b:= proc(n, m) option remember; `if`(n=0,
a(m), m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> `if`(n<3, 1, b(n-3, 0)):
seq(a(n), n=0..25); # Alois P. Heinz, Aug 13 2021
MATHEMATICA
a[0] = a[1] = a[2] = 1; a[n_] := a[n] = Sum[StirlingS2[n - 3, k] a[k], {k, 0, n - 3}]; Table[a[n], {n, 0, 25}]
nmax = 25; A[_] = 0; Do[A[x_] = 1 + x + x^2/2 + Integrate[Integrate[Integrate[A[Exp[x] - 1 + O[x]^(nmax + 1)], x], x], x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] Range[0, nmax]!
PROG
(PARI) lista(nn) = {my(va = vector(nn, k, 1)); for (n=4, nn, va[n] = sum(k=0, n-3, stirling(n-4, k, 2)*va[k+1]); ); va; } \\ Michel Marcus, Jul 06 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 05 2020
STATUS
approved