A097297 Seventh column (m=6) of (1,6)-Pascal triangle A096956.

6, 37, 133, 364, 840, 1722, 3234, 5676, 9438, 15015, 23023, 34216, 49504, 69972, 96900, 131784, 176358, 232617, 302841, 389620, 495880, 624910, 780390, 966420, 1187550, 1448811, 1755747, 2114448, 2531584, 3014440, 3570952, 4209744

Offset

0,1

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) = A096956(n+6, 6) = 6*b(n) - 5*b(n-1) = (n+36)*binomial(n+5, 5)/6, with b(n) = A000579(n+6) = binomial(n+6, 6).

G.f.: (6-5*x)/(1-x)^7.

From Amiram Eldar, Oct 26 2025: (Start)

Sum_{n>=0} 1/a(n) = 146700621098688109/710272942165987200.

Sum_{n>=0} (-1)^n/a(n) = 34752*log(2)/2387 - 77709791089409483729/7813002363825859200. (End)

Mathematica

A097297[n_] := (n + 36)*Binomial[n + 5, 5]/6;
Array[A097297, 50, 0] (* Paolo Xausa, May 02 2025 *)

Crossrefs

Cf. A000579, A096956.

Cf. other columns: A096957 (m = 3), A096958 (m = 4), A096959 (m = 5), A097298 (m = 7), A097299 (m = 8), A097300 (m = 9).

Sequence in context: A346356 A003351 A129651 * A362336 A349857 A047670

Adjacent sequences: A097294 A097295 A097296 * A097298 A097299 A097300

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 13 2004

Status

approved