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

0,4

LINKS

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

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

Cf. A111537, A111546, A111556, A167872

Sequence in context: A076785 A110506 A114189 * A059110 A100326 A303728

Adjacent sequences:  A200656 A200657 A200658 * A200660 A200661 A200662

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Nov 20 2011

STATUS

approved

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Last modified January 24 09:02 EST 2022. Contains 350534 sequences. (Running on oeis4.)