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Search: id:A111529
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| 1, 1, 4, 22, 148, 1156, 10192, 99688, 1069168, 12468208, 157071424, 2126386912, 30797423680, 475378906432, 7793485765888, 135284756985472, 2479535560687360, 47860569736036096, 970606394944476160
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OFFSET
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0,3
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FORMULA
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G.f.: (1/2)*Log(Sum_{n>=0} (n+1)!*x^n) = Sum_{n>=1} a(n)*x^n/n. G.f.: A(x) = 1/(1+2*x - 3*x/(1+3*x - 4*x/(1+4*x -... (continued fraction).
a(n)=Sum_{k,0<=k<=n}2^(n-k)*A089949(n,k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 16 2006
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EXAMPLE
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(1/2)*Log(1 + 2*x + 6*x^2 +... + (n+1)!/1!*x^n +...)
= x + 4/2*x^2 + 22/3*x^3 + 148/4*x^4 + 1156/5*x^5 +...
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, if(n==0, 1, (n/2)*polcoeff(log(sum(m=0, n, (m+1)!/1!*x^m)), n)))}
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CROSSREFS
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Cf: A111528 (table), A104980 (row 1), A111530 (row 3), A111531 (row 4), A111532 (row 5), A111533 (row 6), A111534 (diagonal).
Sequence in context: A121394 A005039 A112898 this_sequence A039304 A062817 A000307
Adjacent sequences: A111526 A111527 A111528 this_sequence A111530 A111531 A111532
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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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