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Search: id:A156325
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| A156325 |
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E.g.f.: A(x) = exp( Sum_{n>=1} n(n+1)/2 * a(n-1)*x^n/n! ) = Sum_{n>=0} a(n)*x^n/n! with a(0)=1. |
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+0
3
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| 1, 1, 4, 34, 482, 10056, 286372, 10591372, 491169996, 27826318000, 1887581200256, 150885500428224, 14028718134958936, 1500672248541122944, 182987661921689610000, 25231215606822797450176
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n) = Sum_{k=1..n} k(k+1)/2 * C(n-1,k-1)*a(k-1)*a(n-k) for n>0, with a(0)=1.
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EXAMPLE
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E.g.f: A(x) = 1 + x + 4*x^2/2! + 34*x^3/3! + 482*x^4/4! + 10056*x^5/5! +...
log(A(x)) = x + 3*1*x^2/2! + 6*4*x^3/3! + 10*34*x^4/4! + 15*482*x^5/5! +...
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PROGRAM
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(PARI) {a(n)=if(n==0, 1, n!*polcoeff(exp(sum(k=1, n, k*(k+1)/2*a(k-1)*x^k/k!)+x*O(x^n)), n))}
(PARI) {a(n)=if(n==0, 1, sum(k=1, n, k*(k+1)/2*binomial(n-1, k-1)*a(k-1)*a(n-k)))}
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CROSSREFS
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Cf. A156326, A156327.
Sequence in context: A071213 A052629 A151919 this_sequence A111169 A002105 A081972
Adjacent sequences: A156322 A156323 A156324 this_sequence A156326 A156327 A156328
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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), Feb 08 2009
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