A323207 - OEIS

%I #8 Feb 26 2019 03:58:01

%S 1,2,4,10,33,141,752,4825,36027,305132,2879840,29909421,338479429,

%T 4139716658,54339861530,761150445734,11322139144239,178116143657889,

%U 2952831190016238,51423702126549166,938126972940647197,17883424301972473339

%N a(n) = Sum_{k=0..n} hypergeometric([-k, k + 1], [-k - 1], n - k).

%F a(n) = Sum_{k=0..n} A323206(n-k, k).

%F a(n) = Sum_{k=0..n} Sum_{j=0..k} A238762(2*j, 2*k)*(n-k)^j.

%F 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).

%p # The function ballot is defined in A238762.

%p A323207 := n -> add(add(ballot(2*j, 2*k)*(n-k)^j, j=0..k), k=0..n):

%p seq(A323207(n), n=0..21);

%t a[n_] := Sum[Hypergeometric2F1[-k, k + 1, -k - 1, n - k], {k, 0, n}];

%t Table[a[n], {n, 0, 21}]

%Y Cf. A323206, A238762.

%K nonn

%O 0,2

%A _Peter Luschny_, Feb 25 2019