A141615 Inverse binomial transform of A120070.

3, 5, -8, 21, -47, 84, -108, 53, 207, -876, 2289, -5097, 10770, -22720, 48489, -103569, 217292, -440178, 848628, -1533887, 2542431, -3695469, 4141675, -1365090, -10867236, 46576386, -135501531, 338590821, -778823106, 1704048861, -3617744616, 7553704652, -15651526743, 32346059748, -66772731098

Offset

0,1

Links

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

Formula

a(n) = Sum_{k=0..n} (-1)^(n+k)*binomial(n,k)*A120070(k). - G. C. Greubel, Sep 22 2024

Mathematica

A120070 = Table[n^2 - k^2, {n, 2, 100}, {k, n-1}]//Flatten;
A141615[n_]:= Sum[(-1)^(n+k)*Binomial[n, k]*A120070[[k+1]], {k, 0, n}];
Table[A141615[n], {n, 0, 40}] (* G. C. Greubel, Sep 22 2024 *)

Prog

(Magma)
A120070:= [n^2-k^2: k in [1..n-1], n in [2..100]];
A141615:= func< n | (&+[(-1)^(n+k)*Binomial(n, k)*A120070[k+1]: k in [0..n]]) >;
[A141615(n): n in [0..40]]; // G. C. Greubel, Sep 22 2024
(SageMath)
A120070=flatten([[n^2 -k^2 for k in range(1, n)] for n in range(2, 101)])
def A141615(n): return sum((-1)^(n+k)*binomial(n, k)*A120070[k] for k in range(n+1))
[A141615(n) for n in range(41)] # G. C. Greubel, Sep 22 2024

Crossrefs

Cf. A120070, A141595.

Sequence in context: A112656 A002366 A377254 * A075192 A361089 A101984

Adjacent sequences: A141612 A141613 A141614 * A141616 A141617 A141618

Keyword

sign,easy

Author

Paul Curtz, Aug 23 2008

Extensions

More terms from N. J. A. Sloane, Jan 25 2011

Status

approved