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 A193683 Alternating row sums of Sheffer triangle A143495 (3-restricted Stirling2 numbers). 1
 1, 2, 3, 1, -14, -59, -99, 288, 2885, 10365, 1700, -226313, -1535203, -4258630, 17243695, 284513877, 1688253890, 2750940953, -51540956455, -624352447488, -3470378651847, -496964048927, 204678286709292, 2311290490508227, 12611758414937801 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In order to have a lower triangular Sheffer matrix for A143495 one uses row and column offsets 0 (not 3). REFERENCES See A143495. LINKS FORMULA E.g.f.: exp(-exp(x)+3*x+1). G.f.: (1 - 2/E(0))/x where E(k) = 1 + 1/(1 - 2*x/(1 - 2*(k+1)*x/E(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Sep 20 2012 G.f.: 1/U(0) where U(k) = 1 - x*(k+2) + x^2*(k+1)/U(k+1); (continued fraction, 1-step). - Sergei N. Gladkovskii, Oct 11 2012 G.f.: (1 - G(0) )/(x+1) where G(k) =  1 - 1/(1-k*x-3*x)/(1-x/(x+1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jan 17 2013 G.f.: 1/Q(0), where Q(k) = 1 - 3*x + x/(1 - x*(k+1)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Apr 22 2013 EXAMPLE Row no. 3 of A143495 with [0,0] offset is [27,37,12,1], hence a(3)=27-37+12-1=1. MATHEMATICA With[{nn=30}, CoefficientList[Series[Exp[3x+1-Exp[x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jan 10 2013 *) CROSSREFS Cf. A143495, A074051 (2-restricted Stirling2 case). Sequence in context: A204137 A102583 A030780 * A145643 A145142 A137738 Adjacent sequences:  A193680 A193681 A193682 * A193684 A193685 A193686 KEYWORD sign,easy AUTHOR Wolfdieter Lang, Oct 06 2011 STATUS approved

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