OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..364
FORMULA
a(n) ~ c * d^n * (n-1)!, where d = 2/(LambertW(2*exp(-2))*(2 + LambertW(2*exp(-2)))) and c = 0.1589194832536846052272420789649724553661575944775731783119884812477... - Vaclav Kotesovec, Oct 05 2020
MAPLE
f:= proc(n) add(binomial(k*(k+1)/2, k)*binomial(k*(k+1)/2, n-k), k=ceil((sqrt(8*n+9)-3)/2)..n) end proc:
map(f, [$0..20]); # Robert Israel, Jun 07 2018
MATHEMATICA
Join[{1}, Table[Sum[Binomial[(k(k+1))/2, k]Binomial[(k(k+1))/2, n-k], {k, n}], {n, 20}]] (* Harvey P. Dale, Jul 09 2018 *)
PROG
(PARI) a(n)=sum(k=0, n, binomial(k*(k+1)/2, k)*binomial(k*(k+1)/2, n-k))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 31 2008
STATUS
approved