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 A128230 Expansion of exp(x)/(1 - x - x^2/2!), where a(n) = 1 + n*a(n-1) + C(n,2)*a(n-2). 3
 1, 2, 6, 25, 137, 936, 7672, 73361, 801705, 9856342, 134640146, 2023140417, 33163934641, 588936102860, 11263023492372, 230783643185881, 5044101110058737, 117136294344278346, 2880200768035996990 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA a(n) ~ n!*exp(sqrt(3)-1)*((1+sqrt(3))/2)^(n+1)/sqrt(3) . - Vaclav Kotesovec, Oct 20 2012 EXAMPLE E.g.f.: exp(x)/(1 - x - x^2/2!) = 1 + 2*x + 6*x^2/2! + 25*x^3/3! + 137*x^4/4! + 936*x^5/5! + 7672*x^6/6! +... + a(n)*x^n/n! +... where a(n) = 1 + n*a(n-1) + n*(n-1)*a(n-2)/2. MATHEMATICA CoefficientList[Series[E^x/(1-x-x^2/2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 20 2012 *) PROG (PARI) a(n)=n!*polcoeff(exp(x+x*O(x^n))/(1-x-x^2/2! +x*O(x^n)), n) CROSSREFS Cf. A087214, A000629, A128231, A128232. Sequence in context: A020010 A102812 A020100 * A084784 A255841 A197772 Adjacent sequences:  A128227 A128228 A128229 * A128231 A128232 A128233 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 20 2007 STATUS approved

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Last modified May 26 13:17 EDT 2022. Contains 354092 sequences. (Running on oeis4.)