OFFSET
0,4
COMMENTS
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
M = an infinite lower triangular matrix with A156791: (1, 1, 6, 7, 78, ...) in every column.
Q = an infinite lower triangular matrix with A006973 prefaced with a 1 as the main diagonal: (1, 1, 2, 9, 24, 130, 720, 8505, ...) and the rest zeros.
Sum_{k=0..n} T(n, k) = A006973(n+1).
T(n, 0) = T(n+1, 1) = A156791(n).
EXAMPLE
First few rows of the triangle:
1,
1, 1;
6, 1, 2;
7, 6, 2, 9;
78, 7, 12, 9, 24;
420, 78, 14 54, 24, 130;
6872, 420, 156, 63, 144, 130, 720;
17253, 6872, 840, 702, 168, 780, 720, 8505;
326552, 17253, 13744, 3780, 1872, 910, 4320, 8505, 35840;
...
Example: Row 4 = (7, 6, 2, 9) = termwise products of (7, 6, 1, 1) and (1, 1, 2, 9).
MATHEMATICA
A006973[n_]:= A006973[n]= If[n<4, Max[n-1, 0], (n-1)!*(1 + Sum[k*(-A006973[k]/k!)^(n/k), {k, Most[Divisors[n]]}])];
S[n_, x_]:= Sum[A006973[j]*x^j, {j, 0, n+2}];
A156791:= With[{p=100}, CoefficientList[Series[S[p, x]/(x + S[p, x]), {x, 0, p}], x]]
Table[A156792[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jun 11 2021 *)
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson, Feb 15 2009
EXTENSIONS
Typo in last line of triangle corrected by Olivier Gérard, Aug 11 2016
STATUS
approved