OFFSET
0,4
LINKS
Branko Dragovich, On Summation of p-Adic Series, arXiv:1702.02569 [math.NT], 2017.
N. J. A. Sloane, Transforms
FORMULA
E.g.f. satisfies A' = exp(x) A - 1.
Recurrence: a(1)=0, a(2)=1, for n > 2, a(n) = 1 + Sum_{j=2..n-1} binomial(n-1, j)*a(j). - Jon Perry, Apr 26 2005
G.f. A(x) satisfies: A(x) = 1 - x * (1 - A(x/(1 - x)) / (1 - x)). - Ilya Gutkovskiy, Jul 10 2020
MATHEMATICA
a[0] = 1; a[1] = 0; a[n_] := a[n] = 1 + Sum[Binomial[n-1, j]*a[j], {j, 2, n-1}]; Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Oct 08 2013, after Jon Perry *)
nmax = 20; Assuming[x > 0, CoefficientList[Series[E^(E^x) * (1/E + ExpIntegralEi[-1] - ExpIntegralEi[-E^x]), {x, 0, nmax}], x] ] * Range[0, nmax]! (* Vaclav Kotesovec, Jul 10 2020 *)
PROG
(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1 - x * (1 - subst(A, x, x/(1-x)) / (1 - x))); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", ")) \\ Vaclav Kotesovec, Jul 10 2020
CROSSREFS
KEYWORD
nonn,nice,easy,eigen
AUTHOR
Joe K. Crump (joecr(AT)carolina.rr.com)
STATUS
approved