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A278463 Triangle T(n,k) read by rows: coefficients of polynomials P_n(t) defined in Formula section.

%I A278463 #19 Jan 18 2017 21:46:34
%S A278463 1,2,2,3,9,4,4,36,44,12,5,110,355,250,48,6,300,2010,3480,1644,240,7,
%T A278463 777,9625,32235,35728,12348,1440,8,1960,42056,242200,498512,390880,
%U A278463 104544,10080,9,4860,173754,1605744,5466321,7745220,4581036,986256,80640,10,11880,691620,9807840,51506490,117711720,123330680,57537360,10265760,725760
%N A278463 Triangle T(n,k) read by rows: coefficients of polynomials P_n(t) defined in Formula section.
%H A278463 Gheorghe Coserea, <a href="/A278463/b278463.txt">Rows n = 1..101, flattened</a>.
%H A278463 F. Chapoton, F. Hivert, J.-C. Novelli, <a href="http://arxiv.org/abs/1307.0092">A set-operad of formal fractions and dendriform-like sub-operads</a>, arXiv preprint arXiv:1307.0092 [math.CO], 2013.
%F A278463 A(x;t) = Sum {n>=1} P_n(t)*x^n/n! = (t-1)*log(1-x) - log(-x + exp(t*log(1-x))) - x.
%F A278463 A278458(x;t) = serreverse(A(-x;t))(-x).
%F A278463 A098558(n-1) = P_n(0), A032184(n) = P_n(1).
%F A278463 A052881(n) = T(n,n-1).
%e A278463 A(x;t) = x + (2*t+2)*x^2/2! + (3*t^2+9*t+4)*x^3/3! + (4*t^3+36*t^2+44*t+12)*x^4/4! + ...
%e A278463 Triangle starts:
%e A278463 n\k  [1]      [2]      [3]      [4]      [5]      [6]      [7]
%e A278463 [1]  1;
%e A278463 [2]  2,       2;
%e A278463 [3]  3,       9,       4;
%e A278463 [4]  4,       36,      44,      12;
%e A278463 [5]  5,       110,     355,     250,     48;
%e A278463 [6]  6,       300,     2010,    3480,    1644,    240;
%e A278463 [7]  7,       777,     9625,    32235,   35728,   12348,   1440;
%e A278463 [8]  ...
%o A278463 (PARI)
%o A278463 N=11; x = 'x+O('x^N);
%o A278463 concat(apply(p->Vec(p), Vec(serlaplace((t-1)*log(1-x) - log(-x + exp(t*log(1-x))) - x))))
%K A278463 nonn,tabl
%O A278463 1,2
%A A278463 _Gheorghe Coserea_, Jan 18 2017