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Search: id:A126470
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| A126470 |
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Triangle, read by rows, where row n lists coefficients of q in F(n,q) that satisfies: F(n,q) = Sum_{k=0..n-1} C(n-1,k)*F(k,q)*F(n-k-1,q)*q^k for n>0, with F(0,q) = 1; row sums equal the factorials: F(n,1) = n!. |
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+0
5
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| 1, 1, 1, 1, 1, 3, 1, 1, 1, 6, 7, 5, 3, 1, 1, 1, 10, 25, 25, 26, 11, 12, 5, 3, 1, 1, 1, 15, 65, 110, 136, 117, 92, 70, 43, 32, 17, 12, 5, 3, 1, 1, 1, 21, 140, 385, 616, 784, 694, 687, 478, 411, 255, 222, 127, 91, 50, 39, 17, 12, 5, 3, 1, 1, 1, 28, 266, 1106, 2471, 4032, 4887, 5189
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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Limit of reversed rows equals A126471. Largest term in rows equal A126472.
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EXAMPLE
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Number of terms in row n is: n*(n-1)/2 + 1.
Row functions B(n,q) begin:
F(0,q) = F(1,q) = 1;
F(1,q) = 1 + q;
F(2,q) = 1 + 3*q + q^2 + q^3;
F(3,q) = 1 + 6*q + 7*q^2 + 5*q^3 + 3*q^4 + q^5 + q^6.
Triangle begins:
1;
1;
1, 1;
1, 3, 1, 1;
1, 6, 7, 5, 3, 1, 1;
1, 10, 25, 25, 26, 11, 12, 5, 3, 1, 1;
1, 15, 65, 110, 136, 117, 92, 70, 43, 32, 17, 12, 5, 3, 1, 1;
1, 21, 140, 385, 616, 784, 694, 687, 478, 411, 255, 222, 127, 91, 50, 39, 17, 12, 5, 3, 1, 1; ...
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PROGRAM
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(PARI) {F(n, q)=if(n==0, 1, sum(k=0, n-1, binomial(n-1, k)*F(k, q)*F(n-k-1, q)*q^k))} {T(n, k)=Vec(F(n, q)+O(q^(n*(n-1)/2+1)))[k+1]}
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CROSSREFS
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Cf. A126471, A126472; Bell number variant: A126347.
Sequence in context: A080002 A058057 A124372 this_sequence A102480 A140670 A068845
Adjacent sequences: A126467 A126468 A126469 this_sequence A126471 A126472 A126473
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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), Dec 31 2006
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