A367548 a(n) = Sum_{k = 0..n} binomial(-n, k) * 2^(n - k).

1, 1, 3, -2, 19, -54, 222, -804, 3075, -11630, 44458, -170268, 654766, -2524508, 9758556, -37802952, 146724579, -570450078, 2221230066, -8660901612, 33811886394, -132148736148, 517012584036, -2024632609272, 7935337877454, -31126450260204, 122183595168612

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = 4^n*3^(-n) - binomial(-n, n+1) * hypergeom([1, 2*n+1], [n + 2], -1/2) / 2.

a(n) = [x^n] (3 + 12*x + sqrt(4*x + 1)*(4*x + 3))/(6 + 16*x - 32*x^2).

D-finite with recurrence 9*n*a(n) +6*(6*n-7)*a(n-1) +16*(-n-4)*a(n-2) +32*(-2*n+5)*a(n-3)=0. - R. J. Mathar, Jan 11 2024

Maple

seq(add(binomial(-n, k)*2^(n - k), k = 0..n), n = 0..26);

Mathematica

Table[Sum[Binomial[-n, k]2^(n-k), {k, 0, n}], {n, 0, 30}] (* Harvey P. Dale, Apr 03 2024 *)

Crossrefs

Cf. A032443.

Sequence in context: A223881 A206582 A154262 * A154261 A098655 A065038

Adjacent sequences: A367545 A367546 A367547 * A367549 A367550 A367551

Keyword

sign

Author

Peter Luschny, Nov 29 2023

Status

approved