OFFSET
0,2
FORMULA
a(n) ~ 2^(2*n) * n^(n - 1/2) / (sqrt(Pi*(1+c)) * c^(n + 1/2) * (2+c)^n * exp(n - 1/2 + c^2/8)), where c = LambertW(2*exp(-2)) = 0.21771510575709011079475830443...
MATHEMATICA
Table[Sum[Binomial[n, k]*Binomial[(k+1)^2, n], {k, 0, n}], {n, 0, 20}]
PROG
(PARI) a(n) = sum(k=0, n, binomial(n, k) * binomial((k+1)^2, n)); \\ Michel Marcus, Jul 09 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 09 2021
STATUS
approved