A228192 a(n) = A001850(n^2), where A001850 forms the central Delannoy numbers.

1, 3, 321, 1462563, 252055236609, 1569245074591690083, 345299757825442889707393857, 2653337188651000290233505189314055363, 706829476163540077094231781323762631545566527489, 6496844758902641761809431955916116052361210081093847336070467

Offset

0,2

Links

Table of n, a(n) for n=0..9.

Formula

a(n) = Sum_{k=0..n^2} binomial(n^2, k) * binomial(n^2+k, k).

a(n) = [x^(n^2)] 1/sqrt(1 - 6*x + x^2).

Equals the logarithmic derivative of A228193, after ignoring the initial term.

Example

 L.g.f.: L(x) = 3*x + 321*x^2/2 + 1462563*x^3/3 + 252055236609*x^4/4 +...
where exponentiation yields the g.f. of A228193:
exp(L(x)) = 1 + 3*x + 165*x^2 + 488007*x^3 + 63015285321*x^4 + 313849204040245803*x^5 +...+ A228193(n)*X^n +...

Prog

 (PARI) {a(n)=sum(k=0, n^2, binomial(n^2, k)*binomial(n^2+k, k))}
for(n=0, 20, print1(a(n), ", "))
(PARI) {A001850(n)=polcoeff(1/sqrt(1 - 6*x + x^2 + x*O(x^n)), n)}
{a(n)=A001850(n^2)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A228193, A001850.

Sequence in context: A168440 A067667 A080976 * A272318 A320284 A235334

Adjacent sequences: A228189 A228190 A228191 * A228193 A228194 A228195

Keyword

nonn

Author

Paul D. Hanna, Aug 15 2013

Status

approved