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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
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
KEYWORD
nonn,eigen
AUTHOR
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.)