The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A155493 Triangle T(n, k) = binomial(n+1, k)*A142459(n+1, k+1)/(k+1), read by rows. 3
1, 1, 1, 1, 15, 1, 1, 118, 118, 1, 1, 770, 3540, 770, 1, 1, 4671, 67810, 67810, 4671, 1, 1, 27321, 1039689, 3085355, 1039689, 27321, 1, 1, 156220, 14006244, 99524810, 99524810, 14006244, 156220, 1, 1, 878868, 173788752, 2602528824, 6090918372, 2602528824, 173788752, 878868, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
T(n, k) = binomial(n+1, k)*t(n, k, m)/(k+1), where t(n,k,m) = (m*(n-k)+1)*t(n-1,k-1,m) + (m*k-m+1)*t(n-1,k,m), t(n,1,m) = t(n,n,m) = 1, and m = 4.
From G. C. Greubel, Apr 01 2022: (Start)
T(n, k) = binomial(n+1, k)*A142459(n+1, k+1)/(k+1).
T(n, n-k) = T(n, k). (End)
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 15, 1;
1, 118, 118, 1;
1, 770, 3540, 770, 1;
1, 4671, 67810, 67810, 4671, 1;
1, 27321, 1039689, 3085355, 1039689, 27321, 1;
1, 156220, 14006244, 99524810, 99524810, 14006244, 156220, 1;
1, 878868, 173788752, 2602528824, 6090918372, 2602528824, 173788752, 878868, 1;
MATHEMATICA
t[n_, k_, m_]:= t[n, k, m]= If[k==1 || k==n, 1, (m*n-m*k+1)*t[n-1, k-1, m] + (m*k -(m -1))*t[n-1, k, m]];
T[n_, k_, m_]:= Binomial[n+1, k]*t[n+1, k+1, m]/(k+1);
Table[T[n, k, 4], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 01 2022 *)
PROG
(Sage)
@CachedFunction
def t(n, k, m):
if (k==1 or k==n): return 1
else: return (m*(n-k)+1)*t(n-1, k-1, m) + (m*k-m+1)*t(n-1, k, m)
def T(n, k, m): return binomial(n+1, k)*t(n+1, k+1, m)/(k+1)
flatten([[T(n, k, 4) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Apr 01 2022
CROSSREFS
Cf. A001263 (m=0), A155467 (m=1), A155491 (m=3), this sequence (m=4).
Cf. A142459.
Sequence in context: A111805 A238754 A176226 * A156939 A174187 A174693
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Jan 23 2009
EXTENSIONS
Edited by G. C. Greubel, Apr 01 2022
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)