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A155857 Row sums of triangle A155856. 3
1, 2, 6, 23, 107, 590, 3786, 27821, 230869, 2137978, 21873854, 245151555, 2987967551, 39358156310, 557259550034, 8440866957273, 136211005966889, 2333068710452146, 42276699542130166, 808068680469402095 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For positive n, a(n) equals the permanent of the n X n matrix with 2's along the main diagonal and the upper diagonal, and 1's everywhere else. [John M. Campbell, Jul 09 2011]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

G.f.: 1/(1-x-x/(1-x-x/(1-x-2x/(1-x-2x/(1-x-3x/(1-x-3x/(1-... (continued fraction);

a(n) = sum{k=0..n, C(2n-k,k)*(n-k)!}.

a(n) = sum{k=0..n, C(n+k,2k)*k!}. [Paul Barry, May 28 2009]

Conjecture: a(n) +(-n-1)*a(n-1) +(n-3)*a(n-2) +a(n-3)=0. - R. J. Mathar, Nov 15 2012

a(n) ~ exp(2) * n!. - Vaclav Kotesovec, Feb 08 2014

MATHEMATICA

Table[Sum[Binomial[2*n-k, k]*(n-k)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 08 2014 *)

CROSSREFS

Sequence in context: A071075 A007555 A101053 * A071076 A297196 A112501

Adjacent sequences:  A155854 A155855 A155856 * A155858 A155859 A155860

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Jan 29 2009

STATUS

approved

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Last modified February 28 05:46 EST 2020. Contains 332321 sequences. (Running on oeis4.)