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 A323207 a(n) = Sum_{k=0..n} hypergeometric([-k, k + 1], [-k - 1], n - k). 2
 1, 2, 4, 10, 33, 141, 752, 4825, 36027, 305132, 2879840, 29909421, 338479429, 4139716658, 54339861530, 761150445734, 11322139144239, 178116143657889, 2952831190016238, 51423702126549166, 938126972940647197, 17883424301972473339 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..21. FORMULA a(n) = Sum_{k=0..n} A323206(n-k, k). a(n) = Sum_{k=0..n} Sum_{j=0..k} A238762(2*j, 2*k)*(n-k)^j. a(n) = Sum_{k=0..n} Sum_{j=0..n-k} (binomial(2*(n-k)-j, n-k) - binomial(2*(n-k)-j, n-k+1))*k^(n-k-j). MAPLE # The function ballot is defined in A238762. A323207 := n -> add(add(ballot(2*j, 2*k)*(n-k)^j, j=0..k), k=0..n): seq(A323207(n), n=0..21); MATHEMATICA a[n_] := Sum[Hypergeometric2F1[-k, k + 1, -k - 1, n - k], {k, 0, n}]; Table[a[n], {n, 0, 21}] CROSSREFS Cf. A323206, A238762. Sequence in context: A154219 A173489 A089476 * A327424 A220028 A006397 Adjacent sequences: A323204 A323205 A323206 * A323208 A323209 A323210 KEYWORD nonn AUTHOR Peter Luschny, Feb 25 2019 STATUS approved

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Last modified September 11 06:30 EDT 2024. Contains 375814 sequences. (Running on oeis4.)