A370982 a(n) = Sum_{k=0..n} 2^(n - k)*Pochhammer(k/2, n - k). Row sums of A370419(n - k, k).

1, 1, 2, 6, 27, 173, 1464, 15414, 193901, 2834337, 47182518, 880910414, 18225754839, 413835006621, 10230048547292, 273473280803598, 7860479860630329, 241731205891735649, 7919436892637421066, 275351783014543431222, 10126387847107625874803, 392728180939713131370669

Offset

0,3

Links

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

Formula

From Vaclav Kotesovec, Mar 12 2024: (Start)

Recurrence: (n-4)*a(n) = (4*n^2 - 24*n + 33)*a(n-1) - (2*n - 5)*(2*n^2 - 12*n + 17)*a(n-2) + (4*n^3 - 40*n^2 + 134*n - 151)*a(n-3) - (n-3)*(2*n - 7)*a(n-4).

a(n) ~ 2^(n - 1/2) * n^(n-1) / exp(n) * (1 + sqrt(Pi)/(2*sqrt(n))). (End)

Mathematica

a[n_] :=  Sum[2^(n - k)*Pochhammer[k/2, n - k], {k, 0, n}]; Array[a, 22, 0] (* Hugo Pfoertner, Mar 06 2024 *)

Crossrefs

Cf. A370419, A371079, A000522.

Sequence in context: A291979 A070076 A227222 * A130455 A372346 A005270

Adjacent sequences: A370979 A370980 A370981 * A370983 A370984 A370985

Keyword

nonn

Author

Peter Luschny, Mar 06 2024

Status

approved