A381940 - OEIS

%I #13 Mar 11 2025 07:57:06

%S 1,2,7,51,440,4170,41921,438972,4736281,52286520,587774685,6705201456,

%T 77426676892,903251324476,10629495065550,126032922655030,

%U 1504194199010435,18056321542477095,217859030049153565,2640609137351540510,32137554969392230950,392580762083089376630

%N G.f. A(x) satisfies A(x) = (1 + x) * B(x*A(x)), where B(x) is the g.f. of A002293.

%F a(n) = Sum_{k=0..n} binomial(5*k+1,k) * binomial(k+1,n-k)/(5*k+1).

%F a(n) = A365184(n) + A365184(n-1).

%o (PARI) a(n) = sum(k=0, n, binomial(5*k+1, k)*binomial(k+1, n-k)/(5*k+1));

%Y Cf. A025227, A381787, A381937.

%Y Cf. A002293, A346647, A365184.

%K nonn,new

%O 0,2

%A _Seiichi Manyama_, Mar 10 2025