A004342 Binomial coefficient C(4n, n-12).

1, 52, 1540, 34220, 635376, 10424128, 156238908, 2186189400, 28987537150, 368136785016, 4513667845896, 53752237906276, 624668654531480, 7110542499799200, 79515468511191440, 875691012480893280, 9516306085765295355, 102217581419177646300, 1086744939880326302940

Offset

12,2

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.

Links

Vincenzo Librandi, Table of n, a(n) for n = 12..100

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Formula

D-finite with recurrence -3*(3*n+10)*(n+4)*(n-12)*(3*n+11)*a(n) + 8*n*(4*n-3)*(2*n-1)*(4*n-1)*a(n-1) = 0. - R. J. Mathar, Mar 19 2025

a(n) ~ 2^(8*n+1/2) / (3^(3*n+25/2) * sqrt(Pi*n)). - Amiram Eldar, Sep 07 2025

Mathematica

Table[Binomial[4n, n-12], {n, 12, 30}] (* Harvey P. Dale, May 05 2011 *)

Prog

(Magma) [Binomial(4*n, n-12): n in [12..50]]; // Vincenzo Librandi, May 06 2011

Crossrefs

Sequence in context: A017715 A112008 A275102 * A230530 A188389 A169997

Adjacent sequences: A004339 A004340 A004341 * A004343 A004344 A004345

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved