A162476 Expansion of (1/(1-x))*c(x/(1-x)^4), c(x) the g.f. of A000108.

1, 2, 8, 39, 205, 1136, 6548, 38882, 236260, 1462131, 9184413, 58408588, 375330536, 2433325315, 15896742423, 104546968252, 691608993478, 4599024778431, 30724413312953, 206114347293697, 1387917616331135, 9377747277136328

Offset: 0

Author

Paul Barry, Jul 04 2009

Keywords

• easy
• nonn

Comments

Partial sums are A162477. Partial sums of A162475.

Formula

G.f.: 1/(1-x-x/((1-x)^3-x/(1-x-x/((1-x)^3-x/(1-x-x/((1-x)^3-x/(1-... (continued fraction);

a(n) = Sum_{k=0..n} C(n+3k,n-k)*A000108(k).

(n+1)*(2*n-3)*a(n) -(4*n-3)*(4*n-5)*a(n-1) +3*(4*n^2-14*n+11)*a(n-2) +(-8*n^2+40*n-27)*a(n-3) +(2*n-1)*(n-6)*a(n-4) = 0. - R. J. Mathar, Nov 15 2011