A350267 a(n) = n*hypergeom([1, 1 - n, -n], [2], 1) if n >= 1, a(0) = 1.

1, 1, 4, 18, 100, 675, 5376, 49294, 510728, 5894109, 74915740, 1039180186, 15613569324, 252501251743, 4371586879128, 80652138666870, 1579212732426256, 32701859350855769, 713914404925713588, 16384896394304282722, 394340620941231415540, 9929838681717090607611

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = n*A247499(n - 1) for n >= 1.

a(n) = Sum_{k=1..n} binomial(n, k)^2 * k! / (n - k + 1), for n >= 1.

Maple

A350267 := n -> ifelse(n = 0, 1, n)*hypergeom([1, 1 - n, -n], [2], 1):
seq(simplify(A350267(n)), n = 0..21);

Mathematica

a[0] = 1; a[n_] := Sum[Binomial[n, k]^2 * k!/(n - k + 1), {k, 1, n}]; Array[a, 20, 0] (* Amiram Eldar, Jan 09 2022 *)

Prog

(PARI) a(n) = if (n == 0, 1, sum(k=1, n, binomial(n, k)^2 * k! / (n - k + 1))); \\ Michel Marcus, Jan 09 2022 [a(0) corrected by Georg Fischer, Jun 22 2022]

Crossrefs

Row sums of A350266.

Cf. A247499.

Sequence in context: A215522 A201826 A327833 * A064852 A229286 A191365

Adjacent sequences: A350264 A350265 A350266 * A350268 A350269 A350270

Keyword

nonn

Author

Peter Luschny, Jan 09 2022

Status

approved