A137154 a(n) = Sum_{k=0..n} binomial(2^k + n-k-1, n-k); equals the row sums of triangle A137153.

1, 2, 4, 9, 24, 79, 331, 1803, 12954, 123983, 1592513, 27604172, 648528166, 20722205191, 903019659239, 53792176322629, 4388683843024734, 491232972054490915, 75545748143323475653, 15984344095578889888206

Offset

0,2

Comments

Matrix inverse of A137153 is A137156.

Links

Table of n, a(n) for n=0..19.

Formula

G.f.: Sum_{n>=0} x^n/(1-x)^(2^n). - Paul D. Hanna, Sep 15 2009

G.f.: Sum_{n>=0} ( (-log(1 - x))^n / n! ) / (1 - 2^n*x). - Paul D. Hanna, Jan 23 2021

Mathematica

Table[Sum[Binomial[2^(n-k) + k - 1, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jan 23 2021 *)

Prog

(PARI) a(n)=sum(k=0, n, binomial(2^k+n-k-1, n-k))
(PARI) {a(n)=local(A=sum(k=0, n, x^k/(1-x+x*O(x^n))^(2^k))); polcoeff(A, n)} \\ Paul D. Hanna, Sep 15 2009

Crossrefs

Cf. A137153, A137155, A137156.

Sequence in context: A135934 A343032 A210342 * A098448 A006406 A097656

Adjacent sequences: A137151 A137152 A137153 * A137155 A137156 A137157

Keyword

nonn

Author

Paul D. Hanna, Jan 24 2008

Status

approved