A278463 Triangle T(n,k) read by rows: coefficients of polynomials P_n(t) defined in Formula section.
1, 2, 2, 3, 9, 4, 4, 36, 44, 12, 5, 110, 355, 250, 48, 6, 300, 2010, 3480, 1644, 240, 7, 777, 9625, 32235, 35728, 12348, 1440, 8, 1960, 42056, 242200, 498512, 390880, 104544, 10080, 9, 4860, 173754, 1605744, 5466321, 7745220, 4581036, 986256, 80640, 10, 11880, 691620, 9807840, 51506490, 117711720, 123330680, 57537360, 10265760, 725760
Offset: 1
Examples
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! + ... Triangle starts: n\k [1] [2] [3] [4] [5] [6] [7] [1] 1; [2] 2, 2; [3] 3, 9, 4; [4] 4, 36, 44, 12; [5] 5, 110, 355, 250, 48; [6] 6, 300, 2010, 3480, 1644, 240; [7] 7, 777, 9625, 32235, 35728, 12348, 1440; [8] ...
Links
- Gheorghe Coserea, Rows n = 1..101, flattened.
- F. Chapoton, F. Hivert, J.-C. Novelli, A set-operad of formal fractions and dendriform-like sub-operads, arXiv preprint arXiv:1307.0092 [math.CO], 2013.
Programs
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PARI
N=11; x = 'x+O('x^N); concat(apply(p->Vec(p), Vec(serlaplace((t-1)*log(1-x) - log(-x + exp(t*log(1-x))) - x))))