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Search: id:A143805
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| 1, 1, 2, 7, 36, 250, 2229, 24656, 329883, 5233837, 96907908, 2066551242, 50196458429, 1375782397859, 42203985613593, 1438854199059479, 54180508061067099, 2241000820010271224, 101316373253530824771
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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1;
1, 1;
2, 3, 1;
6, 11, 6, 1;
24, 50, 35, 10, 1;
...
Shift the entire triangle down 1 place, with T(0,0) = 1. Let T = the new triangle: (1; 1; 1, 1; 2, 3, 1;...).
Sequence A143805 = Lim_{n -> inf.} T^n as a vector.
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FORMULA
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Given triangle A130534:
E.g.f.: Sum_{n>=0} a(n)*x^n/n! = 1 + Sum_{n>=1} a(n-1)*(-log(1-x))^n/n!. [From Paul D. Hanna (pauldhanna(AT)juno.com), May 20 2009]
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EXAMPLE
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Contribution from Paul D. Hanna (pauldhanna(AT)juno.com), May 20 2009: (Start)
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 36*x^4/4! + 250*x^5/5! +...
A(x) = 1 - log(1-x) + log(1-x)^2/2! - 2*log(1-x)^3/3! + 7*log(1-x)^4/4! - 36*log(1-x)^5/5! +-... (End)
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PROGRAM
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(PARI) {a(n)=local(A=[1]); for(i=1, n, A=Vec(serlaplace(1+sum(k=1, #A, A[k]*(-log(1-x+x*O(x^n)))^k/k!)))); A[n+1]} [From Paul D. Hanna (pauldhanna(AT)juno.com), May 20 2009]
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CROSSREFS
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A143806
Sequence in context: A007889 A125033 A034430 this_sequence A112293 A090352 A123549
Adjacent sequences: A143802 A143803 A143804 this_sequence A143806 A143807 A143808
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008
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EXTENSIONS
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Extended by Paul D. Hanna (pauldhanna(AT)juno.com), May 20 2009
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