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A163845 Row sums of triangle A163842. 1
1, 13, 109, 765, 4881, 29369, 169919, 956237, 5272945, 28632525, 153638211, 816715073, 4309138419, 22598433555, 117926579385, 612863125965, 3174156512865 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = sum{k=0..n} sum{i=k..n} binomial(n-k,n-i)*(2i+1)$

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

LINKS

Table of n, a(n) for n=0..16.

Peter Luschny, Swinging Factorial.

MAPLE

swing := proc(n) option remember; if n = 0 then 1 elif

irem(n, 2) = 1 then swing(n-1)*n else 4*swing(n-1)/n fi end:

a := proc(n) local i, k; add(add(binomial(n-k, n-i)*swing(2*i+1), i=k..n), k=0..n) end:

CROSSREFS

Cf. A163842.

Sequence in context: A002648 A055840 A243417 * A075143 A005769 A042941

Adjacent sequences:  A163842 A163843 A163844 * A163846 A163847 A163848

KEYWORD

nonn

AUTHOR

Peter Luschny, Aug 06 2009

STATUS

approved

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Last modified May 23 16:31 EDT 2017. Contains 286925 sequences.