A227235 G.f.: Sum_{n>=1} x^n / (1-x)^prime(n).

1, 3, 7, 16, 38, 96, 262, 767, 2346, 7315, 22954, 72239, 228484, 730470, 2379669, 7960733, 27453387, 97418566, 353442491, 1300699953, 4821108695, 17903653177, 66375491706, 245111697148, 900578294735, 3292301955863, 11991348060873, 43624020578230, 159059383244035, 583396507916927

Offset

1,2

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = Sum_{k=1..n} binomial(prime(k) + n-k-1, n-k).

Example

G.f.: A(x) = x + 3*x^2 + 7*x^3 + 16*x^4 + 38*x^5 + 96*x^6 + 262*x^7 + 767*x^8 +...
where
A(x) = x/(1-x)^2 + x^2/(1-x)^3 + x^3/(1-x)^5 + x^4/(1-x)^7 + x^5/(1-x)^11 + x^6/(1-x)^13 + x^7/(1-x)^17 + x^8/(1-x)^19 +...+ x^n/(1-x)^prime(n) +...

Prog

(PARI) {a(n)=polcoeff(sum(m=1, n, x^m/(1-x+x*O(x^n))^prime(m)), n)}
for(n=1, 40, print1(a(n), ", "))
(PARI) {a(n) = sum(k=1, n, binomial(prime(k)+n-k-1, n-k))}
for(n=1, 40, print1(a(n), ", "))

Crossrefs

Cf. A227234, A000040.

Sequence in context: A211278 A364625 A196154 * A304937 A152090 A190528

Adjacent sequences: A227232 A227233 A227234 * A227236 A227237 A227238

Keyword

nonn

Author

Paul D. Hanna, Jul 14 2013

Status

approved