A137647 a(n) = Sum_{k=0..n} C(k(k+1), k) * C(k(k+1), n-k).

1, 2, 19, 312, 7710, 254226, 10490141, 519862812, 30075235131, 1989376821840, 148089577059957, 12251856625291758, 1115218087275339166, 110758226370052793778, 11918195995470354683205

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..333

Formula

a(n) ~ c * d^n * (n-1)!, where d = 4/(LambertW(2*exp(-2))*(2 + LambertW(2*exp(-2)))) and c = 0.26357096872357954619128367188797403780111321551104973353361235838... - Vaclav Kotesovec, Oct 05 2020

Mathematica

Table[Sum[Binomial[k(k+1), k]Binomial[k(k+1), n-k], {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Dec 11 2018 *)

Prog

(PARI) a(n)=sum(k=0, n, binomial(k*(k+1), k)*binomial(k*(k+1), n-k))

Crossrefs

Sequence in context: A094476 A304637 A119773 * A233107 A187659 A308330

Adjacent sequences: A137644 A137645 A137646 * A137648 A137649 A137650

Keyword

nonn

Author

Paul D. Hanna, Jan 31 2008

Status

approved