A360885 - OEIS

A360885

G.f. satisfies A(x) = 1 + x * A(x * (1 + x^2)).

1, 1, 1, 1, 2, 4, 7, 16, 39, 93, 246, 671, 1884, 5578, 16887, 52854, 170649, 563703, 1914366, 6649798, 23610987, 85689987, 317054427, 1196183592, 4595744763, 17965311672, 71426213637, 288535755417, 1183807706841, 4929801601890, 20825803784129, 89210585925338

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OFFSET

0,5

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..934

FORMULA

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1-2*k,k) * a(n-1-2*k).

PROG

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\3, binomial(i-1-2*j, j)*v[i-2*j])); v;

CROSSREFS

Cf. A127782, A360886.

Cf. A360896.