A378858 G.f. A(x) satisfies A(x) = ( 1 + x/(1 - x*A(x)^(3/4)) )^4.

1, 4, 10, 32, 119, 468, 1934, 8256, 36135, 161276, 731158, 3357748, 15587004, 73021200, 344786056, 1639145180, 7839483967, 37692820908, 182087119582, 883358016328, 4301799946048, 21021519618724, 103049029114618, 506608410994868, 2497162797380145, 12338908560964968

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

G.f.: A(x) = (1 + x*B(x))^4 where B(x) is the g.f. of A364742.

If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).

Prog

(PARI) a(n, r=4, s=1, t=0, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A364742, A365119, A378730.

Cf. A005554, A378801.

Sequence in context: A028283 A196991 A151746 * A110145 A185631 A174520

Adjacent sequences: A378853 A378854 A378856 * A378859 A378860 A378861

Keyword

nonn

Author

Seiichi Manyama, Dec 09 2024

Status

approved