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A086620 Symmetric square table of coefficients, read by antidiagonals, where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = 1/(1-x-y) + xy*f(x,y)^2. 4
1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 14, 7, 1, 1, 9, 28, 28, 9, 1, 1, 11, 47, 79, 47, 11, 1, 1, 13, 71, 175, 175, 71, 13, 1, 1, 15, 100, 331, 504, 331, 100, 15, 1, 1, 17, 134, 562, 1196, 1196, 562, 134, 17, 1, 1, 19, 173, 883, 2464, 3514, 2464, 883, 173, 19, 1, 1, 21, 217 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Determinants of upper left n X n matrices results in A086619: {1,2,10,150,7650,1438200,1051324200,...}, which is the products of the first n terms of the binomial transform of Catalan numbers (A007317): {1,2,5,15,51,188,731,2950,...}.

LINKS

Table of n, a(n) for n=0..68.

FORMULA

Contribution from Paul Barry, Feb 04 2009: (Start)

T(n,k)=sum{j=0..n+k, C(k,j-k)*C(n+2k-j,k)*if(k<=j,A000108(n-k),0)};

Regarded as a number triangle read by row, columns are generated by sum{j=0..k, C(k,j)*A000108(j)*x^j}*x^k/(1-x)^(k+1). (End)

EXAMPLE

Rows begin:

1,_1,__1,__1,___1,____1,____1,_____1, ...

1,_3,__5,__7,___9,___11,___13,____15, ...

1,_5,_14,_28,__47,___71,__100,___134, ...

1,_7,_28,_79,_175,__331,__562,___883, ...

1,_9,_47,175,_504,_1196,_2464,__4572, ...

1,11,_71,331,1196,_3514,_8764,_19244, ...

1,13,100,562,2464,_8764,26172,_67740, ...

1,15,134,883,4572,19244,67740,204831, ...

CROSSREFS

Cf. A086621 (diagonal), A086622 (antidiagonal sums), A086619 (determinants).

Sequence in context: A106597 A108359 A100936 * A338934 A228356 A253670

Adjacent sequences:  A086617 A086618 A086619 * A086621 A086622 A086623

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Jul 24 2003

STATUS

approved

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Last modified April 17 11:26 EDT 2021. Contains 343064 sequences. (Running on oeis4.)