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A167884
Triangle read by rows: T(n,k) given by T(n, 1) = T(n,n) = 1, otherwise T(n, k) = (m*n-m*k+1)*T(n-1,k-1) + (m*k-m+1)*T(n-1,k), where m = 8.
7
1, 1, 1, 1, 18, 1, 1, 179, 179, 1, 1, 1636, 6086, 1636, 1, 1, 14757, 144362, 144362, 14757, 1, 1, 132854, 2941135, 7218100, 2941135, 132854, 1, 1, 1195735, 55446309, 277509955, 277509955, 55446309, 1195735, 1, 1, 10761672, 1001178268, 9211047544, 18315657030, 9211047544, 1001178268, 10761672, 1
OFFSET
1,5
LINKS
G. Strasser, Generalisation of the Euler adic, Math. Proc. Camb. Phil. Soc. 150 (2010) 241-256, Triangle A_8(n,k)
FORMULA
T(n, k) = (m*n-m*k+1)*T(n-1,k-1) + (m*k-m+1)*T(n-1,k), with T(n, 1) = T(n, n) = 1, and m = 8.
Sum_{k=1..n} T(n, k) = A084948(n-1).
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 18, 1;
1, 179, 179, 1;
1, 1636, 6086, 1636, 1;
1, 14757, 144362, 144362, 14757, 1;
1, 132854, 2941135, 7218100, 2941135, 132854, 1;
1, 1195735, 55446309, 277509955, 277509955, 55446309, 1195735, 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]];
A167884[n_, k_]:= T[n, k, 8];
Table[A167884[n, k], {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Mar 18 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 A167884(n, k): return T(n, k, 8)
flatten([[ A167884(n, k) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Mar 18 2022
CROSSREFS
For m = ...,-2,-1,0,1,2,3,4,5,6,7,8, ... we get ..., A225372, A144431, A007318, A008292, A060187, A142458, A142459, A142460, A142461, A142462, A167884, ...
Cf. A084948 (row sums).
Sequence in context: A202677 A179838 A174678 * A022181 A015144 A040332
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Nov 14 2009
EXTENSIONS
Edited by N. J. A. Sloane, May 08 2013
STATUS
approved