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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: A171992 A158884 A053525 * A113869 A084357 A075729

Adjacent sequences:  A208673 A208674 A208675 * A208677 A208678 A208679

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 14 2012

STATUS

approved

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Last modified September 2 23:10 EDT 2014. Contains 246369 sequences.