login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A107668 Column 0 of triangle A107667. 7
1, 4, 45, 816, 20225, 632700, 23836540, 1048592640, 52696514169, 2976295383100, 186548057815801, 12845016620629488, 963644465255618276, 78224633235142116240, 6830914919397129328500, 638477522900795994967040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Shift right of column 1 of triangle A107670, which is the matrix square of triangle A107667.

Given g.f. A(x), the o.g.f. of A304322 equals 1/(1 - x*A(x)).

LINKS

Table of n, a(n) for n=0..15.

FORMULA

O.g.f. A(x) satisfies: [x^n] exp( n^2*x ) * (1 - x*A(x)) = 0 for n>0. - Paul D. Hanna, May 12 2018

a(n) = (n+1)^2 * A107669(n).

a(n) = (n+1)^(2*n+2)/(n+1)! - Sum_{k=1..n} (n+1)^(2*k)/k! * a(n-k) for n>0 with a(0)=1. - Paul D. Hanna, May 12 2018

EXAMPLE

O.g.f.: A(x) = 1 + 4*x + 45*x^2 + 816*x^3 + 20225*x^4 + 632700*x^5 + 23836540*x^6 + 1048592640*x^7 + 52696514169*x^8 + 2976295383100*x^9 + ...

such that the coefficient of x^n in  exp(n^2*x)*(1 - x*A(x))  equals 0 for n>0.

PROG

(PARI) {a(n)=local(A); if(n==0, n+1, A=(n+1)*x+x*O(x^n); for(k=0, n, A+=polcoeff(A, k)*x^k*(n+1-prod(i=0, k, 1+(i-n-1)*x))); polcoeff(A, n))}

for(n=0, 30, print1(a(n), ", "))

(PARI) /* From formula: [x^n] exp( n^2*x ) * (1 - x*A(x)) = 0 */

{a(n) = my(A=[1]); for(i=0, n, A=concat(A, 0); m=#A; A[m] = Vec( exp(x*m^2 +x^2*O(x^m)) * (1 - x*Ser(A)) )[m+1] ); A[n+1]}

for(n=0, 25, print1( a(n), ", ")) \\ Paul D. Hanna, May 12 2018

(PARI) /* From Recurrence: */

{a(n) = if(n==0, 1, (n+1)^(2*n+2)/(n+1)! - sum(k=1, n, (n+1)^(2*k)/k! * a(n-k) ))}

for(n=0, 25, print1( a(n), ", ")) \\ Paul D. Hanna, May 12 2018

CROSSREFS

Cf. A107667, A107669, A107670.

Cf. A304322, A107675, A304394, A304395.

Sequence in context: A304645 A233313 A126747 * A214400 A197989 A276292

Adjacent sequences:  A107665 A107666 A107667 * A107669 A107670 A107671

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 07 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 9 14:04 EDT 2020. Contains 335543 sequences. (Running on oeis4.)