OFFSET
0,6
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Eric Weisstein's World of Mathematics, Laguerre Polynomial
Wikipedia, Laguerre polynomials
FORMULA
E.g.f. of column k: exp(-k*x/(1 - x))/(1 - x).
A(n,k) = n!*Laguerre(n,k).
EXAMPLE
E.g.f. of column k: A_k(x) = 1 + (1 - k)*x/1! + (k^2 - 4*k + 2)*x^2/2! + (-k^3 + 9*k^2 - 18*k + 6)*x^3/3! + (k^4 - 16*k^3 + 72*k^2 - 96*k + 24)*x^4/4! + ...
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 0, -1, -2 -3, -4, ...
2, -1, -2, -1, 2, 7, ...
6, -4, -2, 6, 14, 16, ...
24, -15, 8, 33, 24, -31, ...
120, -56, 88, 102, -104, -380, ...
MATHEMATICA
Table[Function[k, n! SeriesCoefficient[Exp[-k x/(1 - x)]/(1 - x), {x, 0, n}]][j - n], {j, 0, 10}, {n, 0, j}] // Flatten
Table[Function[k, n! LaguerreL[n, k]][j - n], {j, 0, 10}, {n, 0, j}] // Flatten
Table[Function[k, n! Hypergeometric1F1[-n, 1, k]][j - n], {j, 0, 10}, {n, 0, j}] // Flatten
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Ilya Gutkovskiy, Nov 21 2017
STATUS
approved