A268648 G.f. A(x) satisfies: 1/(1-x) = Product_{n>=1} A( x^n - x^(n+1) ).

1, 1, 1, 2, 5, 15, 46, 149, 495, 1682, 5806, 20322, 71919, 256936, 925298, 3355509, 12242471, 44906105, 165503745, 612575796, 2276024836, 8485972958, 31739314999, 119054638380, 447759005393, 1688108544222, 6378722610280, 24153083898505, 91633201241544, 348270745289976, 1325907389447937, 5055855150302197, 19307179347881167, 73832434701139921, 282712142418209398, 1083873025643898568, 4160250292584533013, 15986022831150313756, 61491665982535018897

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..222

Formula

a(n) ~ c * 4^n / n^(3/2), where c = 0.197157770057765155... . - Vaclav Kotesovec, Apr 02 2016

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 15*x^5 + 46*x^6 + 149*x^7 + 495*x^8 + 1682*x^9 + 5806*x^10 + 20322*x^11 + 71919*x^12 +...
where
1/(1-x) = A(x-x^2) * A(x^2-x^3) * A(x^3-x^4) * A(x^4-x^5) * A(x^5-x^6) *...
RELATED SERIES.
A(x-x^2) = 1 + x + x^5 - x^6 + 3*x^7 - 3*x^8 + 6*x^9 - 12*x^10 + 33*x^11 +...
A(x^2-x^3) = 1 + x^2 - x^3 + x^4 - 2*x^5 + 3*x^6 - 6*x^7 + 11*x^8 - 22*x^9 +...
A(x^3-x^4) = 1 + x^3 - x^4 + x^6 - 2*x^7 + x^8 + 2*x^9 - 6*x^10 + 6*x^11 +...
A(x^4-x^5) = 1 + x^4 - x^5 + x^8 - 2*x^9 + x^10 + 2*x^12 - 6*x^13 + 6*x^14 +...
...

Prog

(PARI) {a(n) = my(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A] = 1 - Vec( prod(k=1, #A, subst(Ser(A), x, x^k*(1-x))) )[#A] ); A[n+1]}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Sequence in context: A047086 A071731 A360272 * A148360 A148361 A346521

Adjacent sequences: A268645 A268646 A268647 * A268649 A268650 A268651

Keyword

nonn

Author

Paul D. Hanna, Mar 26 2016

Status

approved