A373733 Triangular numbers with tetrahedral indices: a(n) = (1/72) * (n*(n+1)*(n+2)*(n+3)*(n^2+2)).

0, 1, 10, 55, 210, 630, 1596, 3570, 7260, 13695, 24310, 41041, 66430, 103740, 157080, 231540, 333336, 469965, 650370, 885115, 1186570, 1569106, 2049300, 2646150, 3381300, 4279275, 5367726, 6677685, 8243830, 10104760, 12303280

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = A000217(A000292(n)).

a(n) = A000292(n) + A054563(n).

Mathematica

PolygonalNumber[Binomial[Range[2, 50], 3]] (* Paolo Xausa, Jul 22 2024 *)

Prog

(PARI) a(n)=n*(n+1)*(n+2)*(n+3)*(n^2+2)/72 \\ Charles R Greathouse IV, Jul 10 2024
(Python)
from math import comb
def A373733(n): return comb(comb(n+2, 3)+1, 2) # Chai Wah Wu, Jul 10 2024

Crossrefs

Cf. A000292, A000217, A054563.

Sequence in context: A357730 A341989 A341070 * A244871 A162617 A341139

Adjacent sequences: A373730 A373731 A373732 * A373734 A373735 A373736

Keyword

nonn,easy

Author

J.S. Seneschal, Jun 17 2024

Status

approved