A349730 Row sums of A349728.

1, 1, 4, 16, 66, 284, 1296, 6432, 35862, 231652, 1760232, 15629648, 158866436, 1807908216, 22636353856, 308050239360, 4517683948830, 70949359114740, 1187285196326520, 21083306170356720, 395875848847690140, 7835534053016676360, 163032210287312821920

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = hypergeom([1, 1, 1 - n], [1 - 2*n], 1) * binomial(2*n - 1, n - 1) for n >= 1.

a(n) ~ exp(1) * (n-1)! ~ sqrt(2*Pi*n) * (n/e)^(n-1). - Vaclav Kotesovec, Nov 28 2021

D-finite with recurrence +n*(n-1)*a(n) -(n-1)*(n^2+11*n-19)*a(n-1) +2*(6*n^3-n^2-68*n+93)*a(n-2) +2*(-25*n^3+130*n^2-146*n-65)*a(n-3) +4*(20*n^3-182*n^2+531*n-483)*a(n-4) -8*(n-4)*(2*n-9)^2*a(n-5)=0. - R. J. Mathar, Jul 27 2022

Maple

a := n -> `if`(n = 0, 1, add((n - k)!*(k + n - 1)!/((k - 1)!*n!), k = 1..n)):
seq(a(n), n = 0..22);

Mathematica

a[n_] := If[n == 0, 1, Binomial[2 n - 1, n - 1] HypergeometricPFQ[{1, 1, 1 - n}, {1 - 2 n}, 1]]; Table[a[n], {n, 0, 22}]

Crossrefs

Cf. A349728.

Sequence in context: A109034 A110276 A026883 * A151242 A218645 A273582

Adjacent sequences: A349727 A349728 A349729 * A349731 A349732 A349733

Keyword

nonn

Author

Peter Luschny, Nov 27 2021

Status

approved