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A155928
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G.f. satisfies: A(x) = F(x)^2 where F(x) = Sum_{n>=0} A155926(n)*x^n/[n!*(n+1)!/2^n] and A(x) = Sum_{n>=0} a(n)*x^n/[n!*(n+1)!/2^n].
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1
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1, 2, 11, 122, 2302, 66482, 2735721, 152359874, 11048880926, 1012437290342, 114445632250776, 15649612498128050, 2546878326578431588, 486567378291992448726, 107845834421517755737817
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f. satisfies: A(x) = B( x*sqrt(A(x)) )^2 where B(x) = Sum_{n>=0} x^n/[n!*(n+1)!/2^n].
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EXAMPLE
| G.f.: A(x) = 1 + 2*x + 11*x^2/3 + 122*x^3/18 + 2302*x^4/180 + 66482*x^5/2700 +...
G.f.: A(x) = F(x)^2 where:
F(x) = 1 + x + 4*x^2/3 + 37*x^3/18 + 621*x^4/180 + 16526*x^5/2700 +...+ A155926(n)*x^n/[n!*(n+1)!/2^n] +...
G.f. satisfies: A(x) = B( x*sqrt(A(x)) )^2 where:
B(x) = 1 + x + x^2/3 + x^3/18 + x^4/180 + x^5/2700 +...+ x^n/[n!*(n+1)!/2^n] +...
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PROG
| (PARI) {a(n)=local(B=sum(k=0, n, x^k/(k!*(k+1)!/2^k))+x*O(x^n)); polcoeff((serreverse(x/B)/x)^2, n)*n!*(n+1)!/2^n}
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CROSSREFS
| Cf. A155926.
Sequence in context: A197993 A057076 A118794 * A001946 A206401 A193207
Adjacent sequences: A155925 A155926 A155927 * A155929 A155930 A155931
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jan 31 2009
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