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A137646
a(n) = Sum_{k=0..n} C(k*(k+1)/2, k) * C(k*(k+1)/2, n-k).
1
1, 1, 4, 29, 339, 5406, 109159, 2664399, 76219485, 2499425650, 92402751894, 3801481338219, 172231146665554, 8520038462375370, 456913020454609665, 26402792230144908683, 1635399597258002744628, 108090275300425856404653
OFFSET
0,3
LINKS
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))
KEYWORD
nonn
AUTHOR
Paul D. Hanna,Jan 31 2008
STATUS
approved