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A158909
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Riordan array (1/((1-x)(1-x^2)),x/(1-x)^2).
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2
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1, 1, 1, 2, 3, 1, 2, 7, 5, 1, 3, 13, 16, 7, 1, 3, 22, 40, 29, 9, 1, 4, 34, 86, 91, 46, 11, 1, 4, 50, 166, 239, 174, 67, 13, 1, 5, 70, 296, 553, 541, 297, 92, 15, 1, 5, 95, 496, 1163, 1461, 1068, 468, 121, 17, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Row sums are F(n+1)F(n+2) or A001654(n+1). Diagonal sums are the Jacobsthal numbers A001045.
Transforms r^n into the symmetric third order sequence with g.f. 1/(1-(r+1)x-(r+1)x^2+x^3), see the formulae.
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FORMULA
| From Johannes W. Meijer, Jul 20 2011: (Start)
T(n, k) = sum((-1)^(i+n-k) * binomial(i+2*k+1,i), i=0..n-k)
T(n, k) = A035317(n+k, n-k) = A092879(n, n-k)
sum(T(n,k)*r^k, k=0..n) = coeftayl(1/(1-(r+1)*x-(r+1)*x^2+x^3), x=0, n) (Barry) (End)
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EXAMPLE
| Triangle begins
1,
1, 1,
2, 3, 1,
2, 7, 5, 1,
3, 13, 16, 7, 1,
3, 22, 40, 29, 9, 1,
4, 34, 86, 91, 46, 11, 1,
4, 50, 166, 239, 174, 67, 13, 1
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CROSSREFS
| Sequence in context: A138507 A205699 A109200 * A199915 A183759 A101477
Adjacent sequences: A158906 A158907 A158908 * A158910 A158911 A158912
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 30 2009
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