login
A137647
a(n) = Sum_{k=0..n} C(k(k+1), k) * C(k(k+1), n-k).
1
1, 2, 19, 312, 7710, 254226, 10490141, 519862812, 30075235131, 1989376821840, 148089577059957, 12251856625291758, 1115218087275339166, 110758226370052793778, 11918195995470354683205
OFFSET
0,2
LINKS
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: A375860 A304637 A119773 * A233107 A187659 A308330
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 31 2008
STATUS
approved