A007681 a(n) = (2*n+1)^2*n!. (Formerly M4632)

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

Offset

0,2

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)

Formula

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

Mathematica

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

Crossrefs

Sequence in context: A257589 A341921 A231413 * A279972 A115366 A188210

Adjacent sequences: A007678 A007679 A007680 * A007682 A007683 A007684

Keyword

nonn

Author

N. J. A. Sloane

Status

approved