

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
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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 [condmat.statmech], 2017.
Anthony J. Wood, Richard A. Blythe, Martin R. Evans, Combinatorial mappings of exclusion processes, arXiv:1908.00942 [condmat.statmech], 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(nk,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(n1) + 8*(n1)*(2*n1)*a(n2). (End)


MATHEMATICA

Table[Sum[(n+1)! * (2*n+1)! / ((nk+1)! * (k+1)! * (2*n2*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(nk, 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



