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 A032347 Inverse binomial transform of A032346. 7
 1, 0, 1, 2, 6, 21, 82, 354, 1671, 8536, 46814, 273907, 1700828, 11158746, 77057021, 558234902, 4230337018, 33448622893, 275322101318, 2354401779494, 20878592918183, 191682453823420, 1819147694792802 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A032346, A046934. Sequence in context: A168653 A279567 A281784 * A032346 A329055 A148495 Adjacent sequences:  A032344 A032345 A032346 * A032348 A032349 A032350 KEYWORD nonn,nice,easy,eigen AUTHOR Joe K. Crump (joecr(AT)carolina.rr.com) STATUS approved

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Last modified April 17 14:10 EDT 2021. Contains 343063 sequences. (Running on oeis4.)