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A132427
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Triangle, read by rows of 2n+1 terms, where T(n,k) = T(n,k-1) + T(n-1,k-2) for n>0, 1<k<=2n, with T(n,1)=T(n,0)=T(n-1,2n-2) for n>0 and T(0,0)=1.
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1
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1, 1, 1, 2, 2, 2, 3, 4, 6, 6, 6, 8, 10, 13, 17, 23, 23, 23, 29, 35, 43, 53, 66, 83, 106, 106, 106, 129, 152, 181, 216, 259, 312, 378, 461, 567, 567, 567, 673, 779, 908, 1060, 1241, 1457, 1716, 2028, 2406, 2867, 3434, 3434, 3434, 4001, 4568, 5241, 6020, 6928, 7988
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Column 0 (shift left) equals column 1 and the right-most border.
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FORMULA
| The g.f. of column 0 (A125273) satisfies: G(x) = 1 + x*G( x/(1-x)^2 ) / (1-x). The central terms (A132428) equals the inverse binomial transform of A125273 (offset 1).
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EXAMPLE
| Triangle begins:
1;
1, 1, 2;
2, 2, 3, 4, 6;
6, 6, 8, 10, 13, 17, 23;
23, 23, 29, 35, 43, 53, 66, 83, 106;
106, 106, 129, 152, 181, 216, 259, 312, 378, 461, 567;
567, 567, 673, 779, 908, 1060, 1241, 1457, 1716, 2028, 2406, 2867, 3434; ...
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PROG
| (PARI) {T(n, k)=local(A=[1]); if(2*n<k|k<0, 0, if(n==0&k==0, 1, if(k==0|k==1, T(n-1, 2*n-2), for(i=1, n, A=Vec(Ser(concat([A[ #A], 0], A))/(1-x))); A[k+1])))}
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CROSSREFS
| Cf. A125273; A132428 (central terms).
Sequence in context: A089150 A056697 A176975 * A098523 A048185 A095094
Adjacent sequences: A132424 A132425 A132426 * A132428 A132429 A132430
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 21 2007
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