A155928 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].

1, 2, 11, 122, 2302, 66482, 2735721, 152359874, 11048880926, 1012437290342, 114445632250776, 15649612498128050, 2546878326578431588, 486567378291992448726, 107845834421517755737817

Offset

0,2

Links

Table of n, a(n) for n=0..14.

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].

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] +...

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}

Crossrefs

Cf. A155926.

Sequence in context: A222879 A354978 A247736 * A001946 A121337 A269069

Adjacent sequences: A155925 A155926 A155927 * A155929 A155930 A155931

Keyword

nonn

Author

Paul D. Hanna, Jan 31 2009

Status

approved