login
A200659
Triangle T(n,k), read by rows, given by (1,2,2,3,3,4,4,5,5,6,6,...) DELTA (1,0,1,0,1,0,1,0,1,0,1,0,1,...) where DELTA is the operator defined in A084938.
3
1, 1, 1, 3, 4, 1, 13, 21, 9, 1, 71, 132, 76, 16, 1, 461, 955, 670, 200, 25, 1, 3447, 7782, 6309, 2374, 435, 36, 1, 29093, 70441, 63833, 28413, 6713, 833, 49, 1, 273343, 701352, 694500, 351512, 99868, 16240, 1456, 64, 1
OFFSET
0,4
FORMULA
Sum_{k, 0<=k<=n} T(n,k)*x^k = A153881(n+1), A000007(n), A003319(n), A111537(n), A111546(n), A111556(n), A177354(n-1) for x = -2,-1,0,1,2,3,4 respectively.
Sum_ {k, 0<=k<=n} T(n,k)*x^(n-k) = A000012(n), A111537(n), A167872(n) for x = 0,1,2 respectively.
T(k+1,k)=(k+1)^2.
EXAMPLE
Triangle begins :
1
1, 1
3, 4, 1
13, 21, 9, 1
71, 132, 76, 16, 1
461, 955, 670, 200, 25, 1
3447, 7782, 6309, 2374, 435, 36, 1
29093, 70441, 63833, 28413, 6713, 833, 49, 1
273343, 701352, 694500, 351512, 99868, 16240, 1456, 64, 1
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Nov 20 2011
STATUS
approved