Voozh

A199335

Triangle T(n,k), read by rows, given by (0,1,0,2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,...) DELTA (2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,...), where DELTA is the operator defined in A084938.

1, 0, 2, 0, 2, 4, 0, 2, 14, 8, 0, 2, 36, 66, 16, 0, 2, 82, 342, 262, 32, 0, 2, 176, 1436, 2416, 946, 64, 0, 2, 366, 5364, 16844, 14394, 3222, 128, 0, 2, 748, 18654, 99560, 156190, 76908, 10562, 256

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

Following an observation by Dale Gerdemann, it appears that T(n,k) = A120434(n+1,n-k) for n>=1, k>=1. - M. F. Hasler, Apr 18 2015

See also A144696. - Antti Karttunen, Apr 21 2015

LINKS

Table of n, a(n) for n=0..44.

FORMULA

Sum_k{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A000142(n+1), A162509(n+1) for x=0,1,2 respectively.

Sum_{k, 0<=k<=n} T(n,k)^2^(n-k) = A005649(n).

EXAMPLE