A321608 G.f.: A(x) = Sum_{n>=0} x^n * (1+x)^(2*n^2) / A(x)^n.

1, 1, 2, 5, 22, 100, 581, 3716, 26352, 203664, 1688485, 14922599, 139579911, 1374581231, 14194823072, 153178320198, 1722363891798, 20130227813033, 244028318224686, 3062549991414408, 39723783490631858, 531726501000859625, 7335052105035725087, 104148717578191099492, 1520349684313678309811, 22793632534841442908565, 350622445923759834928352, 5528760266814203384425285

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..200

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 22*x^4 + 100*x^5 + 581*x^6 + 3716*x^7 + 26352*x^8 + 203664*x^9 + 1688485*x^10 + 14922599*x^11 + 139579911*x^12 + ...
such that
A(x) = 1 + x*(1+x)^2/A(x) + x^2*(1+x)^8/A(x)^2 + x^3*(1+x)^18/A(x)^3 + x^4*(1+x)^32/A(x)^4 + x^5*(1+x)^50/A(x)^5 + x^6*(1+x)^72/A(x)^6 + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); A[#A] = Vec(sum(n=0, #A, ((1+x)^n +x*O(x^#A))^(2*n) * x^n/Ser(A)^(n+1) ) )[#A] ); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A303058, A321607.

Sequence in context: A362790 A369830 A056840 * A241345 A272821 A278439

Adjacent sequences: A321605 A321606 A321607 * A321609 A321610 A321611

Keyword

nonn

Author

Paul D. Hanna, Nov 23 2018

Status

approved