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A196148 Antidiagonal sums of square array A111910. 2
1, 2, 7, 30, 146, 772, 4331, 25398, 154158, 961820, 6137734, 39909740, 263665252, 1765815560, 11966535091, 81937361702, 566185489878, 3944202596652, 27676632525362, 195481707009220, 1388890568962556 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..1000

Anthony J. Wood, Richard A. Blythe, Martin R. Evans, Renyi entropy of the totally asymmetric exclusion process, arXiv:1708.00303 [cond-mat.stat-mech], 2017.

Anthony J. Wood, Richard A. Blythe, Martin R. Evans, Combinatorial mappings of exclusion processes, arXiv:1908.00942 [cond-mat.stat-mech], 2019.

FORMULA

Put S(n,k) = (n+k+1)!*(2*n+2*k+1)!/((n+1)!*(k+1)!*(2*n+1)!*(2*k+1)!). Then a(n) = Sum_{k = 0..n} S(n-k,k).

From Vaclav Kotesovec, Dec 16 2017: (Start)

a(n) ~ 2^(3*n+3) / (sqrt(3*Pi) * n^(5/2)).

Recurrence: (n+2)*(2*n+3)*a(n) = 2*(7*n^2 + 7*n + 1)*a(n-1) + 8*(n-1)*(2*n-1)*a(n-2). (End)

MATHEMATICA

Table[Sum[(n+1)! * (2*n+1)! / ((n-k+1)! * (k+1)! * (2*n-2*k+1)! * (2*k+1)!), {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Dec 16 2017 *)

PROG

(PARI) S(n, k) = (n+k+1)!*(2*n+2*k+1)!/((n+1)!*(k+1)!*(2*n+1)!*(2*k+1)!);

a(n) = sum(k = 0, n, S(n-k, k)); \\ Michel Marcus, Dec 16 2017

CROSSREFS

Cf. A111910.

Sequence in context: A006013 A187979 A243632 * A193464 A166990 A059578

Adjacent sequences:  A196145 A196146 A196147 * A196149 A196150 A196151

KEYWORD

nonn,easy

AUTHOR

Peter Bala, Oct 13 2011

STATUS

approved

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)