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Search: id:A111530
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| 1, 1, 5, 33, 261, 2361, 23805, 263313, 3161781, 40907241, 567074925, 8385483393, 131787520101, 2194406578521, 38605941817245, 715814473193073, 13956039627763221, 285509132504621001, 6116719419966460365
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OFFSET
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0,3
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FORMULA
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G.f.: (1/3)*Log(Sum_{n>=0} (n+2)!/2!*x^n) = Sum_{n>=1} a(n)*x^n/n. G.f.: A(x) = 1/(1+3*x - 4*x/(1+4*x - 5*x/(1+5*x -... (continued fraction).
a(n)=Sum_{k, 0<=k<=n}3^(n-k)*A089949(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 16 2006
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EXAMPLE
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(1/3)*Log(1 + 3*x + 12*x^2 +60*x^3+... + (n+2)!/2!*x^n +...)
= x + 5/2*x^2 + 33/3*x^3 + 261/4*x^4 + 2361/5*x^5 +...
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PROGRAM
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(PARI) {a(n)=if(n<0, 0, if(n==0, 1, (n/3)*polcoeff(log(sum(m=0, n, (m+2)!/2!*x^m)), n)))}
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CROSSREFS
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Cf: A111528 (table), A104980 (row 1), A111529 (row 2), A111531 (row 4), A111532 (row 5), A111533 (row 6), A111534 (diagonal).
Sequence in context: A034015 A056159 A061253 this_sequence A087633 A135075 A049377
Adjacent sequences: A111527 A111528 A111529 this_sequence A111531 A111532 A111533
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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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