A137646 a(n) = Sum_{k=0..n} C(k*(k+1)/2, k) * C(k*(k+1)/2, n-k).

1, 1, 4, 29, 339, 5406, 109159, 2664399, 76219485, 2499425650, 92402751894, 3801481338219, 172231146665554, 8520038462375370, 456913020454609665, 26402792230144908683, 1635399597258002744628, 108090275300425856404653

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

Sequence in context: A305636 A276728 A256006 * A231498 A168602 A368452

Adjacent sequences: A137643 A137644 A137645 * A137647 A137648 A137649

Keyword

nonn

Author

Paul D. Hanna, Jan 31 2008

Status

approved