login
A278463
Triangle T(n,k) read by rows: coefficients of polynomials P_n(t) defined in Formula section.
1
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
1,2
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.
FORMULA
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.
A278458(x;t) = serreverse(A(-x;t))(-x).
A098558(n-1) = P_n(0), A032184(n) = P_n(1).
A052881(n) = T(n,n-1).
EXAMPLE
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] ...
PROG
(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))))
CROSSREFS
Sequence in context: A181206 A274959 A143307 * A276248 A322891 A275329
KEYWORD
nonn,tabl
AUTHOR
Gheorghe Coserea, Jan 18 2017
STATUS
approved