A367641 G.f. A(x) satisfies A(x) = (1 + x)^2 + x*A(x)^4 / (1 + x)^3.

1, 3, 10, 64, 504, 4368, 40208, 385728, 3813888, 38590208, 397648384, 4158436864, 44020882944, 470804670464, 5079479547904, 55217003536384, 604200374845440, 6649658071007232, 73560096496779264, 817467602640830464, 9121818467786162176

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..n} binomial(3*k+2,n-k) * binomial(4*k,k)/(3*k+1).

D-finite with recurrence 3*n*(5589*n-14914)*(3*n-1)*(3*n+1)*a(n) +(150903*n^4 -5939762*n^3 +21653157*n^2 -22049842*n +6856944)*a(n-1) +6*(-2312427*n^4 +15333754*n^3 -28367401*n^2 +6040114*n +14892656)*a(n-2) +24*(-3942141*n^4 +46541449*n^3 -199851671*n^2 +367766019*n -243569600)*a(n-3) -32*(n-5)*(8043984*n^3 -85808428*n^2 +305023231*n -361082892)*a(n-4) -384*(n-5)*(n-6)*(885234*n^2 -6808468*n +12951185)*a(n-5) -1536*(n-6)*(n-7)*(144699*n^2 -1203919*n +2337211)*a(n-6) -2048*(n-6)*(n-7)*(n-8)*(27819*n-74186)*a(n-7)=0. - R. J. Mathar, Dec 04 2023

Prog

(PARI) a(n) = sum(k=0, n, binomial(3*k+2, n-k)*binomial(4*k, k)/(3*k+1));

Crossrefs

Cf. A367639, A367640.

Cf. A366267, A366272.

Sequence in context: A160921 A042705 A041014 * A237998 A167939 A352766

Adjacent sequences: A367638 A367639 A367640 * A367642 A367643 A367644

Keyword

nonn

Author

Seiichi Manyama, Nov 25 2023

Status

approved