A097299 Ninth column (m=8) of (1,6)-Pascal triangle A096956.

6, 49, 225, 765, 2145, 5247, 11583, 23595, 45045, 81510, 140998, 234702, 377910, 591090, 901170, 1343034, 1961256, 2812095, 3965775, 5509075, 7548255, 10212345, 13656825, 18067725, 23666175, 30713436, 39516444, 50433900, 63882940

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = A096956(n+8, 8) = 6*b(n) - 5*b(n-1) = (n+48)*binomial(n+7, 7)/8, with b(n) = A000581(n+8) = binomial(n+8, 8).

G.f.: (6-5*x)/(1-x)^9.

From Amiram Eldar, Oct 26 2025: (Start)

Sum_{n>=0} 1/a(n) = 96291226901090927683199789/497202944744241320445303300.

Sum_{n>=0} (-1)^n/a(n) = 20263936*log(2)/248583 - 196135951745684466654648746213/3480420613209689243117123100. (End)

Mathematica

A097299[n_] := (n + 48)*Binomial[n + 7, 7]/8;
Array[A097299, 50, 0] (* Paolo Xausa, May 02 2025 *)

Crossrefs

Cf. A000581, A096956.

Cf. other columns: A096957 (m = 3), A096958 (m = 4), A096959 (m = 5), A097297 (m = 6), A097298 (m = 7), A097300 (m = 9).

Sequence in context: A061429 A048357 A027766 * A283226 A292124 A104170

Adjacent sequences: A097296 A097297 A097298 * A097300 A097301 A097302

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 13 2004

Status

approved