A350290 a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n, k) * binomial(n + k - 1, n - k).

1, 1, -3, -2, 21, -4, -150, 155, 1029, -2072, -6468, 22056, 34122, -208857, -106249, 1816958, -639067, -14629264, 17635800, 108117620, -239571684, -711876496, 2628772968, 3825823888, -25582846134, -10997156129, 227594431035, -98360217830, -1864646227185

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Formula

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

D-finite with recurrence 4*n*(2*n-1)*(9789*n-26254)*a(n) +2*(28924*n^3-27550*n^2-236727*n+284748)*a(n-1) +2*(342172*n^3-1352012*n^2+1027500*n+356439)*a(n-2) -2*(n-3)*(43143*n^2-783097*n+1918735)*a(n-3) -5*(5116*n-30173)*(n-3)*(n-4)*a(n-4)=0. - R. J. Mathar, Jul 27 2022

Maple

a := n -> add((-1)^(n - k)*binomial(n, k)*binomial(n + k - 1, n-k), k = 0..n):
seq(a(n), n = 0..28);

Prog

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*binomial(n+k-1, n-k)); \\ Michel Marcus, Mar 07 2022

Crossrefs

Cf. A109081, A161798, A262440, A262441, A262442.

Sequence in context: A009033 A298661 A323780 * A248123 A018872 A329441

Adjacent sequences: A350287 A350288 A350289 * A350291 A350292 A350293

Keyword

sign

Author

Peter Luschny, Mar 07 2022

Status

approved