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A046803 Triangle of numbers related to Eulerian numbers. 0
1, 1, 2, 1, 6, 3, 1, 14, 22, 4, 1, 30, 105, 65, 5, 1, 62, 416, 581, 171, 6, 1, 126, 1491, 3920, 2695, 420, 7, 1, 254, 5034, 22506, 29310, 11180, 988, 8, 1, 510, 16365, 116667, 256317, 188361, 43041, 2259, 9, 1, 1022, 51892, 564667, 1945297, 2419897, 1090135 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

D. Singh, The numbers L(m,n) and their relations with prepared Bernoulli and Eulerian numbers, Math. Student, 20 (1952), 66-70.

LINKS

Table of n, a(n) for n=1..52.

FORMULA

a(m, n) = Sum C(m, n)*L(m-r, n-1), L = Eulerian numbers.

E.g.f.: exp(x*y)*(exp(x)-1)*(y-1)/(y*exp(x)-exp(x*y)). - Vladeta Jovovic, Sep 20 2003

EXAMPLE

1; 1 2; 1 6 3; 1 14 22 4; ...

MATHEMATICA

egf = Exp[x*y]*(Exp[x]-1)*((y-1)/(y*Exp[x] - Exp[x*y])); row[n_] := Last[ CoefficientList[ Series[egf, {x, 0, n}, {y, 0, n}], {x, y}]]*n!; Flatten[ Table[ row[n], {n, 1, 10}]] (* Jean-Fran├žois Alcover, Dec 20 2012, after Vladeta Jovovic *)

CROSSREFS

Cf. A008292, A046802. Row sums give A002627.

Sequence in context: A034898 A059300 A321331 * A280789 A121468 A168151

Adjacent sequences:  A046800 A046801 A046802 * A046804 A046805 A046806

KEYWORD

nonn,tabl,easy,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vladeta Jovovic, Sep 20 2003

STATUS

approved

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Last modified January 22 05:11 EST 2019. Contains 319353 sequences. (Running on oeis4.)