A184884 Diagonal sums of number triangle A184883.

1, 1, 2, 6, 11, 27, 60, 132, 301, 669, 1502, 3370, 7543, 16919, 37912, 84968, 190457, 426841, 956698, 2144238, 4805827, 10771315, 24141588, 54108332, 121272549, 271806901, 609198390, 1365390546, 3060236911, 6858880431, 15372743856, 34454786384, 77223188593, 173079605553, 387921692082, 869445237846

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,2,-1,1).

Formula

G.f.: (1-x^2)/(1-x-2*x^2-2*x^3+x^4-x^5).

a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..k} C(2*n-4*k,j)*C(k,j)*2^j.

a(n) = Sum_{k=0..floor(n/2)} Hypergeometric2F1([-k, 2*(k-n)], [1], 2). - G. C. Greubel, Nov 19 2021

Mathematica

LinearRecurrence[{1, 2, 2, -1, 1}, {1, 1, 2, 6, 11}, 45] (* G. C. Greubel, Nov 19 2021 *)

Prog

(Magma)
A184883:= func< n, k | (&+[Binomial(k, j)*Binomial(2*(n-k), j)*2^j: j in [0..k]]) >;
A184884:= func< n | (&+[A184883(n, j): j in [0..Floor(n/2)]]) >;
[A184884(n): n in [0..40]]; // G. C. Greubel, Nov 19 2021
(Sage)
def A184883(n, k): return simplify( hypergeometric([-k, 2*(k-n)], [1], 2) )
def A184884(n): return sum( A184883(n, j) for j in (0..n//2) )
[A184884(n) for n in (0..40)] # G. C. Greubel, Nov 19 2021

Crossrefs

Cf. A183883.

Sequence in context: A091622 A362051 A191315 * A275222 A165821 A365046

Adjacent sequences: A184881 A184882 A184883 * A184885 A184886 A184887

Keyword

nonn,easy

Author

Paul Barry, Jan 24 2011

Status

approved