A141595 Binomial transform of A120070.

3, 11, 24, 57, 137, 310, 672, 1445, 3135, 6834, 14797, 31605, 66642, 139500, 291697, 611517, 1285388, 2702278, 5664348, 11813505, 24503911, 50606865, 104273395, 214794252, 442965900, 914940122, 1891691613, 3910617099, 8072908510, 16626013425, 34146007356, 69946108176

Offset: 0

Author

Paul Curtz, Aug 21 2008

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A120070.

Programs

Magma

A120070:= [n^2-k^2: k in [1..n-1], n in [2..100]];
A141595:= func< n | (&+[Binomial(n,k)*A120070[k+1]: k in [0..n]]) >;
[A141595(n): n in [0..40]]; // G. C. Greubel, Sep 15 2024

Mathematica

A120070= Table[n^2 - k^2, {n,2,100}, {k,n-1}]//Flatten;
A141595[n_]:= Sum[Binomial[n, k]*A120070[[k+1]], {k,0,n}];
Table[A141595[n], {n,0,40}] (* G. C. Greubel, Sep 15 2024 *)

SageMath

A120070=flatten([[n^2 -k^2 for k in range(1,n)] for n in range(2,101)])
def A141595(n): return sum(binomial(n,k)*A120070[k] for k in range(n+1))
[A141595(n) for n in range(41)] # G. C. Greubel, Sep 15 2024

Formula

a(n) = Sum_{k=0..n} binomial(n,k)*A120070(k). - G. C. Greubel, Sep 15 2024

Extensions

Terms a(8) onward added by G. C. Greubel, Sep 15 2024