

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
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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

Table of n, a(n) for n=0..52.


FORMULA

Recurrence: T(0,0)=1, T(0,k)=0 for k>0 and for n>=1 T(n,k) = T(n1,k1) + (k+1)*T(n1,k) + (k+2)*T(n1,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..dim1):
for k in (0..n1):
T[n, k] = T[n1, k1]+(k+1)*T[n1, k]+(k+2)*T[n1, k+1]
return T
A216916_triangle(9)


CROSSREFS

Sequence in context: A122919 A188513 A260301 * A157401 A143911 A185422
Adjacent sequences: A216913 A216914 A216915 * A216917 A216918 A216919


KEYWORD

nonn,tabl


AUTHOR

Peter Luschny, Sep 20 2012


STATUS

approved



