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A163842 Triangle interpolating the swinging factorial (A056040) restricted to odd indices with its binomial transform. Same as interpolating the beta numbers 1/beta(n,n) (A002457) with (A163869). 5
1, 7, 6, 43, 36, 30, 249, 206, 170, 140, 1395, 1146, 940, 770, 630, 7653, 6258, 5112, 4172, 3402, 2772, 41381, 33728, 27470, 22358, 18186, 14784, 12012, 221399, 180018, 146290, 118820, 96462, 78276, 63492 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Triangle read by rows. For n >= 0, k >= 0 let

T(n,k) = sum{i=k..n} binomial(n-k,n-i)*(2i+1)$

where i$ denotes the swinging factorial of i (A056040).

REFERENCES

Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Peter Luschny, Swinging Factorial.

EXAMPLE

1

7, 6

43, 36, 30

249, 206, 170, 140

1395, 1146, 940, 770, 630

7653, 6258, 5112, 4172, 3402, 2772

41381, 33728, 27470, 22358, 18186, 14784, 12012

MAPLE

Computes n rows of the triangle. For the functions 'SumTria' and 'swing' see A163840.

a := n -> SumTria(k->swing(2*k+1), n, true);

MATHEMATICA

sf[n_] := n!/Quotient[n, 2]!^2; t[n_, k_] := Sum[Binomial[n-k, n-i]*sf[2*i+1], {i, k, n}]; Table[t[n, k], {n, 0, 7}, {k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Jun 28 2013 *)

CROSSREFS

Row sums are A163845. Cf. A056040, A163650, A163841, A163842, A163840, A002426, A000984.

Sequence in context: A163260 A073112 A070425 * A038272 A249992 A223531

Adjacent sequences:  A163839 A163840 A163841 * A163843 A163844 A163845

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Aug 06 2009

STATUS

approved

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Last modified April 25 19:05 EDT 2017. Contains 285426 sequences.