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 A046803 Triangle of numbers related to Eulerian numbers. 0

%I

%S 1,1,2,1,6,3,1,14,22,4,1,30,105,65,5,1,62,416,581,171,6,1,126,1491,

%T 3920,2695,420,7,1,254,5034,22506,29310,11180,988,8,1,510,16365,

%U 116667,256317,188361,43041,2259,9,1,1022,51892,564667,1945297,2419897,1090135

%N Triangle of numbers related to Eulerian numbers.

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

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

%F E.g.f.: exp(x*y)*(exp(x)-1)*(y-1)/(y*exp(x)-exp(x*y)). - _Vladeta Jovovic_, Sep 20 2003

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

%t 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-François Alcover_, Dec 20 2012, after _Vladeta Jovovic_ *)

%Y Cf. A008292, A046802. Row sums give A002627.

%K nonn,tabl,easy,nice

%O 1,3

%A _N. J. A. Sloane_.

%E More terms from _Vladeta Jovovic_, Sep 20 2003

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Last modified March 26 04:32 EDT 2019. Contains 321481 sequences. (Running on oeis4.)