A180719 Logarithmic derivative of A180718.

1, 5, 16, 61, 226, 884, 3543, 14429, 59623, 248950, 1049159, 4454356, 19032976, 81769735, 352967821, 1529948477, 6655903632, 29050257899, 127162016206, 558088733406, 2455157735151, 10824115727199, 47814658900427

Offset: 1

Author

Paul D. Hanna, Sep 24 2010

Keywords

• nonn

Examples

			L.g.f.: L(x) = x + 5*x^2/2 + 16*x^3/3 + 61*x^4/4 + 226*x^5/5 +...
which equals the sum of the series:
L(x) = (1 + x)^2*x
+ (1 + 4*x + x^2)^2*x^2/2
+ (1 + 9*x + 9*x^2 + x^3)^2*x^3/3
+ (1 + 16*x + 36*x^2 + 16*x^3 + x^4)^2*x^4/4
+ (1 + 25*x + 100*x^2 + 100*x^3 + 25*x^4 + x^5)^2*x^5/5
+ (1 + 36*x + 225*x^2 + 400*x^3 + 225*x^4 + 36*x^5 + x^6)^2*x^6/6 +...
where exponentiation yields the integer series:
exp(L(x)) = 1 + x + 3*x^2 + 8*x^3 + 25*x^4 + 80*x^5 + 271*x^6 + 952*x^7 + 3443*x^8 + 12758*x^9 + 48212*x^10 +...+ A180718(n)*x^n/n +...
		

Crossrefs

Cf. A180718.

Programs

PARI

{a(n)=n*polcoeff(sum(m=1,n,sum(k=0,m,binomial(m,k)^2*x^k)^2*x^m/m)+x*O(x^n),n)}

Formula

L.g.f.: L(x) = Sum_{n>=0} [ Sum_{k=0..n} C(n,k)^2*x^k ]^2*x^n/n.