OFFSET
0,8
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..958 (rows 0..100)
FORMULA
EXAMPLE
Triangle begins:
1;
0, 1;
0, 1;
0, 1, 4;
0, 1, 4;
0, 1, 8;
0, 1, 20, 36;
0, 1, 24, 36;
0, 1, 36, 72;
0, 1, 52, 108;
0, 1, 112, 576, 576;
0, 1, 128, 612, 576;
0, 1, 200, 1116, 1152;
...
The T(5,1) = 1 pattern is 11111.
The T(5,2) = 8 patterns are 12222, 11222, 11122, 11112, 21111, 22111, 22211, 22221.
PROG
(PARI)
P(n) = {Vec(-1 + prod(k=1, n, 1 + y*x^k + O(x*x^n)))}
R(u, k) = {k*[subst(serlaplace(p)/y, y, k-1) | p<-u]}
T(n)={my(u=P(n), v=concat([1], sum(k=1, n, R(u, k)*sum(r=k, n, y^r*binomial(r, k)*(-1)^(r-k)) ))); [Vecrev(p) | p<-v]}
{ my(A=T(16)); for(n=1, #A, print(A[n])) }
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Andrew Howroyd, Feb 12 2022
STATUS
approved