OFFSET
0,6
COMMENTS
Row n contains 1+floor(n/4) terms. Row sums yield A118934. Given column vector V = A118935, then V is invariant under matrix product T*V = V, or, A118935(n) = Sum_{k=0..n} T(n,k)*A118935(k). Given C = Pascal's triangle and T = this triangle, then matrix product M = C^-1*T yields M(4n,n) = (4*n)!/(n!*4^n), 0 otherwise (cf. A100861 formula due to Paul Barry).
LINKS
G. C. Greubel, Rows n = 0..150 of the triangle, flattened
FORMULA
E.g.f.: A(x,y) = exp(x + y*x^4/4).
EXAMPLE
Triangle begins:
1;
1;
1;
1;
1, 6;
1, 30;
1, 90;
1, 210;
1, 420, 1260;
1, 756, 11340;
1, 1260, 56700;
1, 1980, 207900;
1, 2970, 623700, 1247400; ...
MATHEMATICA
T[n_, k_]:= If[n<4*k, 0, n!/(4^k*k!*(n-4*k)!)];
Table[T[n, k], {n, 0, 20}, {k, 0, n/4}]//Flatten (* G. C. Greubel, Mar 07 2021 *)
PROG
(PARI) T(n, k)=if(n<4*k, 0, n!/(k!*(n-4*k)!*4^k))
(Sage)
f=factorial;
flatten([[0 if n<4*k else f(n)/(4^k*f(k)*f(n-4*k)) for k in [0..n/4]] for n in [0..20]]) # G. C. Greubel, Mar 07 2021
(Magma)
F:= Factorial;
[n lt 4*k select 0 else F(n)/(4^k*F(k)*F(n-4*k)): k in [0..Floor(n/4)], n in [0..20]]; // G. C. Greubel, Mar 07 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, May 06 2006
STATUS
approved