login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A274378
G.f. satisfies A(x) = (1 + x*A(x))^2 * (1 + x^2*A(x)^3).
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
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
Sequence in context: A046646 A342284 A174195 * A177521 A152322 A308726
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 04 2016
STATUS
approved