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A155810 Triangle, read by rows, where g.f.: A(x,y) = exp( Sum_{n>=1} (2^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients. 6

%I

%S 1,2,1,10,6,1,188,82,14,1,16774,4452,490,30,1,6745436,1074934,71108,

%T 2602,62,1,11466849412,1082704500,43173414,951300,13002,126,1,

%U 80444398636280,4411700155252,104251164804,1387446246,11470404,62538,254,1,2306003967992402758,72146891831948808,989785148972932,7803708940836,38993810694,129076164,292810,510,1,268654794629082985019564,4724816968764733073446,36967624172237518088,169140002768370820,500466007443108,1001353593606,1382564804,1343434,1022,1

%N Triangle, read by rows, where g.f.: A(x,y) = exp( Sum_{n>=1} (2^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.

%C More generally, for m integer, exp( Sum_{n>=1} (m^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.

%F G.f.: A(x,y) = Sum_{n>=0} Sum_{k>=0} T(n,k)*x^n*y^k.

%e G.f.: A(x,y) = 1 + (2 + y)x + (10 + 6y + y^2)x^2 + (188 + 82y + 14y^2 + y^3)x^3 +...

%e Triangle begins:

%e 1;

%e 2, 1;

%e 10, 6, 1;

%e 188, 82, 14, 1;

%e 16774, 4452, 490, 30, 1;

%e 6745436, 1074934, 71108, 2602, 62, 1;

%e 11466849412, 1082704500, 43173414, 951300, 13002, 126, 1;

%e 80444398636280, 4411700155252, 104251164804, 1387446246, 11470404, 62538, 254, 1;

%e 2306003967992402758, 72146891831948808, 989785148972932, 7803708940836, 38993810694, 129076164, 292810, 510, 1;

%e 268654794629082985019564, 4724816968764733073446, 36967624172237518088, 169140002768370820, 500466007443108, 1001353593606, 1382564804, 1343434, 1022, 1; ...

%o (PARI) {T(n,k)=polcoeff(polcoeff(exp(sum(m=1,n+1,(2^m+y)^m*x^m/m)+x*O(x^n)),n,x),k,y)}

%o for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print(""))

%Y Cf. A155200 (column 0), A155201 (row sums), A155811 (column 1).

%K nonn,tabl

%O 0,2

%A _Paul D. Hanna_, Feb 04 2009

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