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Search: id:A102223
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| 0, 1, 3, 22, 323, 7906, 290262, 14919430, 1022475715, 90094491994, 9923239949978, 1335853771297750, 215797095378591542, 41198645313603207990, 9176288655853717238830, 2358300288047799986966722
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OFFSET
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0,3
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COMMENT
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Triangle A008459 consists of squared binomial coefficients.
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FORMULA
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a(n) = 1 + (1/n)*Sum_{k=0..n-1} C(n, k)^2*k*a(k) for n>0, with a(0)=0.
Sum_{n>=0} a(n)*x^n/n!^2 = -ln(2-BesselI(0,2*sqrt(x))). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 16 2006
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EXAMPLE
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a(2) = 3 = 1 + (1*0*0 + 4*1*1)/2,
a(3) = 22 = 1 + (1*0*0 + 9*1*1 + 9*2*3)/3,
a(4) = 323 = 1 + (1*0*0 + 16*1*1 + 36*2*3 + 16*3*22)/4,
a(5) = 7906 = 1 + (1*0*0 + 25*1*1 + 100*2*3 + 100*3*22 + 25*4*323)/5.
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PROGRAM
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(PARI) a(n)=if(n<1, 0, 1+sum(k=0, n-1, binomial(n, k)^2*k*a(k))/n)
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CROSSREFS
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Cf. A008459, A102220, A102222.
Adjacent sequences: A102220 A102221 A102222 this_sequence A102224 A102225 A102226
Sequence in context: A144681 A124567 A161967 this_sequence A046947 A002485 A099750
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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 2004
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