A132745 Row sums of (A008550 formatted as a triangular array).

1, 2, 3, 5, 11, 32, 114, 467, 2130, 10642, 57629, 335381, 2082582, 13716502, 95352529, 696790819, 5334094259, 42649956716, 355261078352, 3075741331481, 27620835538407, 256810928552476, 2468108094076860, 24481671811988907, 250296546308500181, 2634309876797453868, 28509045368598994348

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Formula

From G. C. Greubel, Feb 16 2021: (Start)

a(n) = Sum_{k=0..n} Hypergeometric2F1([1-n+k, k-n], [2], k).

a(n) = Sum_{k=0..n} Hypergeometric2F1([1-k, -k], [2], n-k).

a(n) = 1 + Sum_{k=1..n} Sum_{j=0..k-1} binomial(k,j)^2 * ((k-j)*(n-k)^j/(k*(j+1))).

a(n) = 1 + Sum_{k=1..n} Sum_{j=0..k-1} A001263(k, k-j) * (n-k)^j. (End)

Mathematica

Table[Sum[Hypergeometric2F1[1-k, -k, 2, n-k], {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, Feb 16 2021 *)

Prog

(Sage)
def A243631(n, k): return 1 if n==0 else sum( binomial(n, j)^2*k^j*(n-j)/(n*(j+1)) for j in [0..n-1])
def A132745(n): return sum( A243631(k, n-k) for k in [0..n] )
[A132745(n) for n in [0..30]] # G. C. Greubel, Feb 16 2021
(Magma)
A243631:= func< n, k | n eq 0 select 1 else (&+[ Binomial(n, j)^2*k^j*(n-j)/(n*(j+1)): j in [0..n-1]]) >;
A132745:= func< n | (&+[A243631(k, n-k): k in [0..n]]) >;
[A132745(n): n in [0..30]]; // G. C. Greubel, Feb 16 2021

Crossrefs

Cf. A001263, A008550, A243631.

Sequence in context: A007097 A173422 A375554 * A124538 A124627 A305971

Adjacent sequences: A132742 A132743 A132744 * A132746 A132747 A132748

Keyword

nonn

Author

Philippe Deléham, Nov 21 2007

Extensions

Terms a(11) onward added by G. C. Greubel, Feb 16 2021

Status

approved