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A199569
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Expansion 1/(1-x^2*cosech(x))=sum(n>=0, a(n)*x^n/n!^2.
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0
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1, 1, 4, 30, 384, 7480, 207360, 7780080, 380190720, 23481311616, 1789201612800, 164904696633600, 18084647927808000, 2327418985883397120, 347368297708734382080, 59514548453599599360000, 11601363342443780505600000, 2552998389393196650531225600
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..17.
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FORMULA
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a(n)=n!^2*sum(m=1..n, m!*sum(i=0..n-m,(2^i*m^(n-m-i)* sum(k=0..i, (stirling2(i,k)*k!*stirling1(m+k,m))/(m+k)!))/(i!*(n-m-i)!))),n>0, a(0)=1.
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EXAMPLE
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1/(1-x^2*csch(x)) = 1 + x + x^2 + (5*x^3)/6 + (2*x^4)/3 + (187*x^5)/360 + (2*x^6)/5 + (4631*x^7)/1512 + (221*x^8)/945 + (11983*x^9)/67200 + (214*x^10)/1575 + ...
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PROG
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a(n) := if n=0 then 1 else n!^2 * sum(m!*sum((2^i*m^(n-m-i)* sum((stirling2(i, k)*k!*stirling1(m+k, m))/(m+k)!, k, 0, i))/(i!*(n-m-i)!), i, 0, n-m), m, 1, n)
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CROSSREFS
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Sequence in context: A166892 A185523 A187736 * A168129 A193500 A163885
Adjacent sequences: A199566 A199567 A199568 * A199570 A199571 A199572
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KEYWORD
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nonn
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AUTHOR
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Vladimir Kruchinin, Nov 08 2011
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STATUS
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approved
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