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Search: id:A103327
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| A103327 |
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Triangle T(n, k) read by rows: binomial(2n+1, 2k+1). |
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+0
7
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| 1, 3, 1, 5, 10, 1, 7, 35, 21, 1, 9, 84, 126, 36, 1, 11, 165, 462, 330, 55, 1, 13, 286, 1287, 1716, 715, 78, 1, 15, 455, 3003, 6435, 5005, 1365, 105, 1, 17, 680, 6188, 19448, 24310, 12376, 2380, 136, 1, 19, 969, 11628, 50388, 92378, 75582, 27132, 3876, 171
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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A subset of Pascal's triangle A007318.
Elements have the same parity as those of Pascal's triangle.
Matrix inverse is A104033. - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 28 2005
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REFERENCES
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A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 224.
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FORMULA
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G.f. for column k is sum{k=0..k+1, C(2(k+1), 2j)x^j)/(1-x)^(2(k+1)) - Paul Barry (pbarry(AT)wit.ie), Feb 24 2005
G.f.: A(x, y) = (1 + x*(1-y))/( (1 + x*(1-y))^2 - 4*x ). - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 28 2005
Sum_{k, 0<=k<=n} T(n, k)*A000364(n-k) = A002084(n) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 27 2005
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EXAMPLE
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1
3,1
5,10,1
7,35,21,1
9,84,126,36,1
11,165,462,330,55,1
13,286,1287,1716,715,78,1
15,455,3003,6435,5005,1365,105,1
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PROGRAM
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(PARI) {T(n, k)=local(X=x+x*O(x^n), Y=y+y*O(y^k)); polcoeff(polcoeff((1+X*(1-Y))/((1+X*(1-Y))^2-4*X), n, x), k, y)} (Hanna)
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CROSSREFS
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Reflected version of A091042. Cf. A086645, A103328.
Cf. A104033.
Sequence in context: A146916 A146255 A122366 this_sequence A065229 A093905 A063853
Adjacent sequences: A103324 A103325 A103326 this_sequence A103328 A103329 A103330
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, Feb 06 2005
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