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
Keywords
Programs
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Mathematica
Table[Sum[Binomial[2^(n-k) + k - 1, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jan 23 2021 *) -
PARI
a(n)=sum(k=0,n,binomial(2^k+n-k-1,n-k))
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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
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
Comments