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A124539
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Triangle, read by rows, where row n equals the inverse binomial transform of column n in the rectangular table A124530.
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1
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1, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 15, 8, 1, 0, 1, 61, 51, 14, 1, 0, 1, 273, 311, 138, 24, 1, 0, 1, 1331, 1901, 1191, 349, 42, 1, 0, 1, 6977, 11838, 9693, 4100, 868, 76, 1, 0, 1, 38872, 75556, 76950, 43257, 13459, 2163, 142, 1, 0, 1, 228089, 495146, 606275, 430517
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| In table A124530, the g.f. of row n, R_n(y), simultaneously satisfies: R_n(y) = Sum_{k>=0} y^k*R_k(y)^(n*k) for n>=0.
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FORMULA
| Secondary diagonal T(n+1,n) = 2^n + 2n.
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EXAMPLE
| Triangle begins:
1;
1, 0;
1, 1, 0;
1, 4, 1, 0;
1, 15, 8, 1, 0;
1, 61, 51, 14, 1, 0;
1, 273, 311, 138, 24, 1, 0;
1, 1331, 1901, 1191, 349, 42, 1, 0;
1, 6977, 11838, 9693, 4100, 868, 76, 1, 0;
1, 38872, 75556, 76950, 43257, 13459, 2163, 142, 1, 0;
1, 228089, 495146, 606275, 430517, 180000, 43274, 5442, 272, 1, 0; ...
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PROG
| (PARI) {T(n, k)=local(m=max(n, k), R); R=vector(m+1, r, vector(m+1, c, if(r==1|c<=2, 1, r^(c-2)))); for(i=0, m, for(r=0, m, R[r+1]=Vec(sum(c=0, m, x^c*Ser(R[c+1])^(r*c)+O(x^(m+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
| Cf. A124530 (table).
Sequence in context: A055105 A200545 A058710 * A096501 A062862 A084119
Adjacent sequences: A124536 A124537 A124538 * A124540 A124541 A124542
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Nov 05 2006
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