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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 August 4 13:49 EDT 2020. Contains 336201 sequences. (Running on oeis4.)