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A008826 Triangle of coefficients from fractional iteration of e^x - 1. 4
1, 1, 3, 1, 13, 18, 1, 50, 205, 180, 1, 201, 1865, 4245, 2700, 1, 875, 16674, 74165, 114345, 56700, 1, 4138, 155477, 1208830, 3394790, 3919860, 1587600, 1, 21145, 1542699, 19800165, 90265560, 182184030, 167310360, 57153600, 1, 115973 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

The triangle reflects the Jordan-decomposition of the matrix of Stirling numbers of the second kind. A display of the matrix formula can be found at the Helms link which also explains the generation rule for the A()-numbers in a different way. - Gottfried Helms Apr 19 2014

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 148.

LINKS

Vincenzo Librandi, Rows n = 2..20, flattened

Gottfried Helms, Answer in mathoverflow.

FORMULA

G.f. A(n;x) for n-th row satisfies A(n;x) = Sum_{k=0..n-1} Stirling2(n, k)*A(k;x)*x, A(1;x) = 1. - Vladeta Jovovic, Jan 02 2004

EXAMPLE

Triangle starts:

  1;

  1,  3;

  1, 13,  18;

  1, 50, 205, 180; ...

MATHEMATICA

a[n_, x_] := Sum[ StirlingS2[n, k]*a[k, x]*x, {k, 0, n-1}]; a[1, _] = 1; Table[ CoefficientList[ a[n, x], x] // Rest, {n, 2, 10}] // Flatten (* Jean-Fran├žois Alcover, Dec 11 2012, after Vladeta Jovovic *)

CROSSREFS

Diagonals give A008827, A006472, A059355. Row sums are A005121.

Sequence in context: A133177 A184828 A053286 * A103440 A116483 A262593

Adjacent sequences:  A008823 A008824 A008825 * A008827 A008828 A008829

KEYWORD

nonn,tabl,nice

AUTHOR

N. J. A. Sloane, Mar 15 1996

EXTENSIONS

More terms from Vladeta Jovovic, Jan 02 2004

STATUS

approved

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Last modified November 15 11:35 EST 2018. Contains 317238 sequences. (Running on oeis4.)