A141595 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

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

FORMULA

a(n) = Sum_{k=0..n} binomial(n,k)*A120070(k). - 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 *)

PROG

(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

(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

CROSSREFS

Cf. A120070.

Sequence in context: A212252 A295622 A294415 * A112051 A231068 A185258

Adjacent sequences: A141592 A141593 A141594 * A141596 A141597 A141598

KEYWORD

nonn,changed

AUTHOR

Paul Curtz, Aug 21 2008

EXTENSIONS

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

STATUS

approved