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Search: id:A126471
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| A126471 |
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Limit of reversed rows of triangle A126470, in which row sums equal the factorials. |
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+0
4
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| 1, 1, 3, 5, 12, 17, 39, 58, 108, 170, 310, 449, 791, 1181, 1960, 2915, 4668, 6822, 10842, 15818, 24254, 35061, 53213, 76061, 113822, 162631, 238660, 337764, 491319, 690530, 994390, 1391968, 1982724, 2757196, 3896450, 5382342, 7546547, 10384787
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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In triangle A126470, 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.
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EXAMPLE
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Row functions F(n,q) of triangle A126470 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.
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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))} {a(n)=Vec(F(n+1, q)+O(q^(n*(n-1)/2+1)))[n*(n-1)/2+1]}
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CROSSREFS
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Cf. A126470, A126472; Bell number variant: A126348.
Sequence in context: A057587 A032438 A025083 this_sequence A024696 A025088 A082740
Adjacent sequences: A126468 A126469 A126470 this_sequence A126472 A126473 A126474
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Dec 31 2006
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