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A184884 Diagonal sums of number triangle A184883. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Jan 24 2011
STATUS
approved

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Last modified June 15 02:34 EDT 2024. Contains 373402 sequences. (Running on oeis4.)