A274378 G.f. satisfies A(x) = (1 + x*A(x))^2 * (1 + x^2*A(x)^3).

1, 2, 6, 24, 111, 552, 2873, 15458, 85312, 480314, 2747845, 15928080, 93347153, 552181372, 3292571913, 19769887128, 119430685503, 725375643416, 4426786390959, 27131644746326, 166932630227613, 1030684209393288, 6383992918008611, 39657230694169284, 247008096338698523, 1542292860296588558, 9651791500807437834, 60528789932966226468, 380333245334293851637, 2394179659042901060436, 15096873553004201457425

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f. satisfies: A(x) = (1/x) * Series_Reversion( x*(1 - x^2*(1+x)^2) / (1+x)^2 ).

G.f. satisfies: A( x*(1 - x^2*(1+x)^2)/(1+x)^2 ) = (1+x)^2/(1 - x^2*(1+x)^2).

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+k,k) * binomial(2*n+2*k+2,n-2*k). - Seiichi Manyama, Jan 27 2024

Example

 G.f.: A(x) = 1 + 2*x + 6*x^2 + 24*x^3 + 111*x^4 + 552*x^5 + 2873*x^6 + 15458*x^7 + 85312*x^8 +...
such that A(x) = 1 + 2*x*A(x) + x^2*(A(x)^2 + A(x)^3) + 2*x^3*A(x)^4 + x^4*A(x)^5.

Prog

(PARI) {a(n) = my(A=1); for(i=1, n, A = (1 + x*A)^2 * (1 + x^2*A^3) + x*O(x^n) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n) = my(A=1); A = (1/x)*serreverse(x*(1-x^2*(1+x)^2)/(1+x +x^2*O(x^n) )^2 ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A181734, A274379.

Sequence in context: A046646 A342284 A174195 * A177521 A152322 A308726

Adjacent sequences: A274375 A274376 A274377 * A274379 A274380 A274381

Keyword

nonn

Author

Paul D. Hanna, Aug 04 2016

Status

approved