A007681 a(n) = (2*n+1)^2*n!.

1, 9, 50, 294, 1944, 14520, 121680, 1134000, 11652480, 130999680, 1600300800, 21115987200, 299376000000, 4539498163200, 73316942899200, 1256675067648000, 22784918188032000, 435717099417600000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• H. W. Gould, A class of binomial sums and a series transform, Utilitas Math., 45 (1994), 71-83.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Delbert L. Johnson, Table of n, a(n) for n = 0..447
• H. W. Gould, A class of binomial sums and a series transform, Utilitas Math., 45 (1994), 71-83. (Annotated scanned copy)

Programs

Mathematica

Table[(2n+1)^2 n!,{n,0,20}] (* Harvey P. Dale, Mar 10 2023 *)

Formula

E.g.f.: (1 + 6*x + x^2)/(1 - x)^3. - Ilya Gutkovskiy, May 12 2017