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

1,2

Links

Table of n, a(n) for n=1..23.

Formula

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

Example

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 +...

Prog

(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)}

Crossrefs

Cf. A180718.

Sequence in context: A098347 A203414 A189450 * A343164 A300317 A307469

Adjacent sequences: A180716 A180717 A180718 * A180720 A180721 A180722

Keyword

nonn

Author

Paul D. Hanna, Sep 24 2010

Status

approved