A379246 G.f. A(x) satisfies A(x) = ( (1 + x*A(x)^3)/(1 - x*A(x)) )^3.

1, 6, 90, 1838, 43362, 1111878, 30101786, 846703950, 24501770370, 724733787206, 21813611057562, 665947742487342, 20571682188676450, 641823879285627654, 20195381326042866138, 640146274715559742670, 20421757641058980395010, 655181707585675667750790, 21125606434257067959841242

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..647

Robert Israel, Linear recurrence of order 31

Formula

G.f.: B(x)^3 where B(x) is the g.f. of A379247.

a(n) = Sum_{k=0..n} binomial(3*n+6*k+3,k) * binomial(4*n+5*k+2,n-k)/(n+2*k+1).

D-finite with recurrence of order 31: see link. - Robert Israel, May 07 2026

Prog

(PARI) a(n) = sum(k=0, n, binomial(3*n+6*k+3, k)*binomial(4*n+5*k+2, n-k)/(n+2*k+1));

Crossrefs

Cf. A365843, A379245.

Cf. A379172, A379247.

Sequence in context: A201073 A006480 A138462 * A002896 A266734 A379255

Adjacent sequences: A379243 A379244 A379245 * A379247 A379248 A379249

Keyword

nonn

Author

Seiichi Manyama, Dec 18 2024

Status

approved