|
Search: id:A106336
|
|
|
| A106336 |
|
Number of ways of writing n as the sum of n+1 triangular numbers, divided by n+1. |
|
+0
5
|
|
| 1, 1, 1, 2, 5, 11, 25, 64, 169, 442, 1172, 3180, 8730, 24116, 67159, 188568, 532741, 1512695, 4315996, 12369324, 35587923, 102747636, 297601382, 864525312, 2518185362, 7353088206, 21520084301, 63115752910, 185474840912
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
FORMULA
|
G.f.: A(x) = (1/x)*serreverse( x*eta(x)/eta(x^2)^2 ). G.f. satisfies: F(x*A(x)) = A(x), where F(x) = Sum_{n>=0} x^(n*(n+1)/2). G.f. satisfies: log(A(x)) = Sum_{n>=1} A106337(n)/n*x^n.
|
|
EXAMPLE
|
The radius of convergence equals r = 0.322627632692191133... (A106335)
at which the g.f. converges to A(r) = 1.987369721184684145... (A106334).
F(x*A(x)) = A(x) where F(x) = 1 + x + x^3 + x^6 + x^10 + x^15 + x^21 + ...
|
|
PROGRAM
|
(PARI) {a(n)=local(X); if(n<0, 0, X=x+x*O(x^n); polcoeff(eta(X^2)^(2*n+2)/eta(X)^(n+1)/(n+1), n))} (PARI) {a(n)=if(n<0, 0, polcoeff( sum(k=1, (sqrtint(8*n+1)+1)\2, x^((k^2-k)/2), x*O(x^n))^(n+1)/(n+1), n))}
|
|
CROSSREFS
|
Cf. A106333, A106334, A106335, A106337.
Sequence in context: A106805 A094981 A097779 this_sequence A047775 A001432 A127075
Adjacent sequences: A106333 A106334 A106335 this_sequence A106337 A106338 A106339
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Apr 29 2005
|
|
|
Search completed in 0.002 seconds
|
