A193532 G.f.: x = Sum_{n>=1} x^n * ((1+x)^(n+1) - x^(n+1)) / (1+x)^a(n).

3, 4, 8, 9, 11, 12, 17, 18, 20, 21, 24, 25, 27, 28, 34, 35, 37, 38, 41, 42, 44, 45, 49, 50, 52, 53, 56, 57, 59, 60, 67, 68, 70, 71, 74, 75, 77, 78, 82, 83, 85, 86, 89, 90, 92, 93, 98, 99, 101, 102, 105, 106, 108, 109, 113, 114, 116, 117, 120, 121, 123, 124, 132, 133, 135, 136, 139, 140, 142, 143, 147, 148, 150, 151, 154, 155, 157, 158, 163, 164, 166, 167, 170

Offset

1,1

Links

Table of n, a(n) for n=1..83.

Formula

a(n) = n + floor(log_2(n+1)) + A011371(n+1) for n>=1, where A011371(n) = highest power of 2 dividing n!.

Example

G.f.: x = x*((1+x)^2 - x^2)/(1+x)^3 + x^2*((1+x)^3 - x^3)/(1+x)^4 + x^3*((1+x)^4 - x^4)/(1+x)^8 + x^4*((1+x)^5 - x^5)/(1+x)^9 + x^5*((1+x)^6 - x^6)/(1+x)^11 + x^6*((1+x)^7 - x^7)/(1+x)^12 + x^7*((1+x)^8 - x^8)/(1+x)^17 + x^8*((1+x)^9 - x^9)/(1+x)^18 +...+ x^n*((1+x)^(n+1) - x^(n+1))/(1+x)^a(n) +...

Prog

(PARI) {a(n)=if(n<1, 0, n+ floor(log(n+1+1/100)/log(2)) + valuation((n+1)!, 2))}
(PARI) {a(n)=if(n<1, 0, if(n==1, 3, polcoeff(sum(m=1, n+1, x^m*((1+x)^(m+1)-x^(m+1))/(1+x +x^2*O(x^n))^if(m>=n, 1, a(m)))+x^(n+1), n+1)))}

Crossrefs

Cf. A193259, A193260.

Sequence in context: A057549 A284392 A047460 * A068056 A006520 A054204

Adjacent sequences: A193529 A193530 A193531 * A193533 A193534 A193535

Keyword

nonn

Author

Paul D. Hanna, Jul 29 2011

Status

approved