A066114 a(0) = 1; for n > 0, a(n) = (n!*(3*n+1))/2.

1, 2, 7, 30, 156, 960, 6840, 55440, 504000, 5080320, 56246400, 678585600, 8861529600, 124540416000, 1874333260800, 30076510464000, 512608352256000, 9247873130496000, 176065276907520000, 3527707911856128000, 74203511249387520000

Offset

0,2

Links

Harry J. Smith, Table of n, a(n) for n = 0..100

Formula

G.f.: Sum_{n>=0} (1 + n*x)^(n+1) / (2 + n*x)^(n+1). - Paul D. Hanna, Oct 26 2014

a(n) = n-th derivative of (1 + 2/x + 3/x^2)/2 at -1. - Luc Rousseau, May 03 2022

Example

G.f.: A(x) = 1 + 2*x + 7*x^2 + 30*x^3 + 156*x^4 + 960*x^5 + 6840*x^6 + ...
where
A(x) = 1/2 + (1+x)^2/(2+x)^2 + (1+2*x)^3/(2+2*x)^3 + (1+3*x)^4/(2+3*x)^4 + (1+4*x)^5/(2+4*x)^5 + (1+5*x)^6/(2+5*x)^6 + (1+6*x)^7/(2+6*x)^7 + ...

Mathematica

Join[{1}, Table[(n!(3n+1))/2, {n, 20}]] (* Harvey P. Dale, Jun 15 2011 *)

Prog

(PARI) { for (n=0, 100, a=(n!*(3*n + 1))/2; if (n==0, a=1); write("b066114.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 01 2010
(PARI) \p200 \\ set precision
{A=Vec(sum(n=0, 600, (1.+n*x)^(n+1)/(2 + n*x +O(x^31))^(n+1)) )}
for(n=1, #A, print1(round(A[n]), ", ")) \\ Paul D. Hanna, Oct 26 2014

Crossrefs

Sequence in context: A030975 A144495 A154259 * A088128 A001053 A124552

Adjacent sequences: A066111 A066112 A066113 * A066115 A066116 A066117

Keyword

nonn,easy

Author

George E. Antoniou, Dec 05 2001

Status

approved