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A193319
G.f.: Sum_{n>=0} x^n*Product_{k=1..n} (1 - (4*k-3)*x) / (1 - (4*k-1)*x).
1
1, 1, 3, 11, 49, 273, 1859, 14731, 131073, 1287041, 13822051, 161149227, 2024636273, 27227371345, 389753084259, 5912210812139, 94679315407489, 1595416629866625, 28204870292970563, 521740077282205387, 10074781737635639601
OFFSET
0,3
LINKS
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 11*x^3 + 49*x^4 + 273*x^5 + 1859*x^6 +...
where
A(x) = 1 + x*(1-x)/(1-3*x) + x^2*(1-x)*(1-5*x)/((1-3*x)*(1-7*x)) + x^3*(1-x)*(1-5*x)*(1-9*x)/((1-3*x)*(1-7*x)*(1-11*x)) +...
PROG
(PARI) {a(n)=polcoeff(sum(m=0, n, x^m*prod(k=1, m, (1-(4*k-3)*x)/(1-(4*k-1)*x +x*O(x^n)))), n)}
CROSSREFS
Sequence in context: A012316 A261600 A331617 * A265905 A058733 A203163
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 22 2011
STATUS
approved