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A216916 Triangle read by rows, T(n,k) for 0<=k<=n, generalizing A098742. 1
1, 1, 1, 3, 3, 1, 9, 12, 6, 1, 33, 51, 34, 10, 1, 135, 237, 193, 79, 15, 1, 609, 1188, 1132, 584, 160, 21, 1, 2985, 6381, 6920, 4268, 1510, 293, 28, 1, 15747, 36507, 44213, 31542, 13576, 3464, 497, 36, 1, 88761, 221400, 295314, 238261, 120206, 37839, 7231, 794 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Full concordance with A098742 would require two zero rows at the top of the triangle which we omitted for simplicity.
Matrix inverse is A137338. - Peter Luschny, Sep 21 2012
LINKS
FORMULA
Recurrence: T(0,0)=1, T(0,k)=0 for k>0 and for n>=1 T(n,k) = T(n-1,k-1) + (k+1)*T(n-1,k) + (k+2)*T(n-1,k+1).
EXAMPLE
[0] [1]
[1] [1, 1]
[2] [3, 3, 1]
[3] [9, 12, 6, 1]
[4] [33, 51, 34, 10, 1]
[5] [135, 237, 193, 79, 15, 1]
[6] [609, 1188, 1132, 584, 160, 21, 1]
[7] [2985, 6381, 6920, 4268, 1510, 293, 28, 1]
[8] [15747, 36507, 44213, 31542, 13576, 3464, 497, 36, 1]
PROG
(Sage)
def A216916_triangle(dim):
T = matrix(ZZ, dim, dim)
for n in range(dim): T[n, n] = 1
for n in (1..dim-1):
for k in (0..n-1):
T[n, k] = T[n-1, k-1]+(k+1)*T[n-1, k]+(k+2)*T[n-1, k+1]
return T
A216916_triangle(9)
CROSSREFS
Sequence in context: A122919 A188513 A260301 * A157401 A143911 A185422
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Sep 20 2012
STATUS
approved

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Last modified March 19 01:22 EDT 2024. Contains 370952 sequences. (Running on oeis4.)