A381909 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * B(x)) ), where B(x) is the g.f. of A002293.

1, 3, 16, 121, 1117, 11569, 128648, 1500054, 18091859, 223794730, 2823369749, 36185653049, 469808971400, 6165903108879, 81667617713170, 1090234962290114, 14654059445570507, 198151602861222385, 2693625234657193038, 36789566028850640226, 504600217464088999466

Offset

0,2

Links

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

Formula

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

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

a(n) = binomial(2*(1 + n), n)*hypergeom([(1+n)/4, (2+n)/4, (3+n)/4, (4+n)/4, -n], [(2+n)/3, (3+n)/3, (4+n)/3, 3+n], -2^8/3^3)/(1 + n). - Stefano Spezia, Mar 10 2025

Prog

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

Crossrefs

Cf. A381908, A381910.

Cf. A002293.

Sequence in context: A120015 A003692 A166883 * A145158 A132070 A362204

Adjacent sequences: A381906 A381907 A381908 * A381910 A381911 A381912

Keyword

nonn

Author

Seiichi Manyama, Mar 10 2025

Status

approved