A162475 Expansion of c(x/(1-x)^4), c(x) the g.f. of A000108.

1, 1, 6, 31, 166, 931, 5412, 32334, 197378, 1225871, 7722282, 49224175, 316921948, 2057994779, 13463417108, 88650225829, 587062025226, 3907415784953, 26125388534522, 175389933980744, 1181803269037438, 7989829660805193

Offset: 0

Author

Paul Barry, Jul 04 2009

Keywords

• easy
• nonn

Crossrefs

Cf. A000108.

Partial sums are A162476.

Formula

G.f.: 1/(1-x/((1-x)^4-x/(1-x/((1-x)^4-x/(1-... (continued fraction);

a(n) = Sum_{k=0..n} C(n+3k-1,n-k)*A000108(k).

Conjecture: (n+1)*a(n) +3*(2-3n)*a(n-1) +2*(7n-20)*a(n-2) +2*(22-5n)*a(n-3) +(5n-31)*a(n-4) +(8-n)*a(n-5)=0. - R. J. Mathar, Nov 17 2011