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Search: id:A111531
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| 1, 1, 6, 46, 416, 4256, 48096, 591536, 7840576, 111226816, 1680157056, 26918720896, 455971214336, 8143926373376, 153013563734016, 3017996904928256, 62369444355076096, 1348096649995841536
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OFFSET
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0,3
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FORMULA
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G.f.: (1/4)*Log(Sum_{n>=0} (n+3)!/3!*x^n) = Sum_{n>=1} a(n)*x^n/n. G.f.: A(x) = 1/(1+4*x - 5*x/(1+5*x - 6*x/(1+6*x -... (continued fraction).
a(n)=Sum_{k, 0<=k<=n}4^(n-k)*A089949(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 16 2006
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EXAMPLE
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(1/4)*Log(1 + 4*x + 20*x^2 + 120*x^3 +... + (n+3)!/3!*x^n +...)
= x + 6/2*x^2 + 46/3*x^3 + 416/4*x^4 + 4256/5*x^5 +...
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, if(n==0, 1, (n/4)*polcoeff(log(sum(m=0, n, (m+3)!/3!*x^m)), n)))}
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CROSSREFS
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Cf: A111528 (table), A104980 (row 1), A111529 (row 2), A111530 (row 3), A111532 (row 5), A111533 (row 6), A111534 (diagonal).
Sequence in context: A073507 A155598 A084772 this_sequence A052781 A049378 A001829
Adjacent sequences: A111528 A111529 A111530 this_sequence A111532 A111533 A111534
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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), Aug 06 2005
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