A084625 Binomial transform of A084624.

1, 3, 8, 21, 55, 143, 366, 919, 2265, 5491, 13125, 31000, 72485, 168042, 386709, 884161, 2009742, 4543830, 10222264, 22891099, 51041560, 113359224, 250839510, 553173006, 1216070081, 2665518207, 5826533103, 12703217438, 27628250142

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} C(n, k)*floor(C(k+5, 5)/C(k+2, 2)).

a(n) = 2^n + Sum_{k=0..n} binomial(n,k)*floor(k*(k^2 +12*k +47)/60). - G. C. Greubel, Mar 24 2023

Mathematica

a[n_]:= a[n]= 2^n +Sum[Binomial[n, j]*Floor[j*(j^2+12*j+47)/60], {j, 0, n}];
Table[a[n], {n, 0, 50}] (* G. C. Greubel, Mar 24 2023 *)

Prog

(Magma)
A084625:= func< n | (&+[Binomial(n, j)*Floor(Binomial(j+5, 3)/10): j in [0..n]]) >;
[A084625(n): n in [0..50]]; // G. C. Greubel, Mar 24 2023
(SageMath)
def A084625(n): return sum(binomial(n, j)*(binomial(j+5, 3)//10) for j in range(n+1))
[A084625(n) for n in range(51)] # G. C. Greubel, Mar 24 2023

Crossrefs

Cf. A084624, A084626, A084627, A084628, A084630, A084631.

Sequence in context: A231222 A231436 A027932 * A088305 A001906 A278613

Adjacent sequences: A084622 A084623 A084624 * A084626 A084627 A084628

Keyword

easy,nonn

Author

Paul Barry, Jun 01 2003

Status

approved