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Search: id:A124469
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| A124469 |
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Triangle, read by rows, where row n equals the inverse binomial transform of column n in the rectangular table A124460. |
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+0
3
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| 1, 1, 1, 1, 3, 1, 1, 8, 6, 1, 1, 22, 28, 11, 1, 1, 65, 120, 81, 20, 1, 1, 209, 500, 494, 219, 37, 1, 1, 730, 2088, 2733, 1812, 578, 70, 1, 1, 2743, 8884, 14411, 12904, 6299, 1518, 135, 1, 1, 10958, 38803, 74484, 84424, 56590, 21384, 4007, 264, 1, 1, 46057, 174366
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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In table A124460, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k * R_k(y)^n for n>=0.
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FORMULA
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Secondary diagonal T(n+1,n) = 2^n + n = A006127(n).
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 3, 1;
1, 8, 6, 1;
1, 22, 28, 11, 1;
1, 65, 120, 81, 20, 1;
1, 209, 500, 494, 219, 37, 1;
1, 730, 2088, 2733, 1812, 578, 70, 1;
1, 2743, 8884, 14411, 12904, 6299, 1518, 135, 1;
1, 10958, 38803, 74484, 84424, 56590, 21384, 4007, 264, 1;
1, 46057, 174366, 383391, 526121, 453082, 238853, 72076, 10693, 521, 1;
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PROGRAM
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(PARI) {T(n, k)=local(R=vector(n+2, r, vector(n+2, c, binomial(r+c-2, c-1)))); for(i=0, n, for(r=0, n, R[r+1]=Vec(sum(c=0, n, x^c*Ser(R[c+1])^r+O(x^(n+1)))))); Vec(subst(Ser(vector(n+1, j, R[j][n+1])), x, x/(1+x))/(1+x))[k+1]}
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CROSSREFS
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Cf. A124470 (row sums), A006127 (diagonal T(n+1, n)); A124460 (table).
Sequence in context: A117425 A091698 A134380 this_sequence A094816 A097712 A034801
Adjacent sequences: A124466 A124467 A124468 this_sequence A124470 A124471 A124472
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Nov 03 2006
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