login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208676 G.f.: 1 = Sum_{n>=1} a(n) * x^n*(1-x)^(n+1) / Product_{k=1..n} (1 + (k+1)*x). 5
1, 1, 4, 23, 169, 1496, 15400, 180055, 2350867, 33840345, 531707256, 9045486916, 165507986668, 3238945135696, 67470601883224, 1489923969768999, 34753006977085479, 853544188578784147, 22011310309759024484, 594514290559650994575, 16780116115165946427561 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Related triangle T=A132623 is generated by sums of matrix powers of itself such that:

T(n,k) = Sum_{j=1..n-k-1} [T^j](n-1,k) with T(n+1,n) = n+1 and T(n,n)=0 for n>=0.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n) = A132623(n+1, 1) / 2.

EXAMPLE

1 = 1*(1-x) + 1*x*(1-x)^2/(1+2*x) + 4*x^2*(1-x)^3/((1+2*x)*(1+3*x)) + 23*x^3*(1-x)^4/((1+2*x)*(1+3*x)*(1+4*x)) + 169*x^4*(1-x)^5/((1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)) +...

PROG

(PARI) {a(n)=if(n<0, 0, polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-x)^(k+1)/prod(j=1, k, 1+(j+1)*x+x*O(x^n))), n))}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A132623, A132624, A208677, A208678.

Sequence in context: A158884 A053525 A277382 * A113869 A084357 A075729

Adjacent sequences:  A208673 A208674 A208675 * A208677 A208678 A208679

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 14 2012

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 10 17:19 EST 2016. Contains 279005 sequences.