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 A000997 From a differential equation. (Formerly M0739 N0277) 5
 0, 1, 0, 0, 1, 2, 3, 5, 12, 36, 110, 326, 963, 2964, 9797, 34818, 130585, 506996, 2018454, 8238737, 34627390, 150485325, 677033911, 3147372610, 15066340824, 74025698886, 372557932434, 1919196902205, 10119758506626, 54627382038761, 301832813494746 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Shifts 3 places left under binomial transform. - Olivier Gérard, Aug 12 2016 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Table of n, a(n) for n=0..30. S. Tauber, On generalizations of the exponential function, Amer. Math. Monthly, 67 (1960), 763-767. FORMULA G.f. A(x) satisfies: A(x) = x*(1 + x^2*A(x/(1 - x))/(1 - x)). - Ilya Gutkovskiy, May 02 2019 MAPLE a := proc(n) option remember; local k; if n<=2 then [0, 1, 0][n+1] else add (binomial(n-3, k)*a(k), k=1..n-3) fi end: seq(a(n), n=0..29); # Sean A. Irvine, Mar 27 2015 MATHEMATICA m = 30; A[_] = 0; Do[A[x_] = x (1 + x^2 A[x/(1 - x)]/(1 - x)) + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Oct 23 2019 *) CROSSREFS Cf. A000995. Sequence in context: A369847 A306038 A008323 * A266541 A301929 A107475 Adjacent sequences: A000994 A000995 A000996 * A000998 A000999 A001000 KEYWORD nonn,eigen AUTHOR N. J. A. Sloane EXTENSIONS More terms from Sean A. Irvine, Mar 27 2015 STATUS approved

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Last modified June 23 20:17 EDT 2024. Contains 373653 sequences. (Running on oeis4.)