A097300 Tenth column (m=9) of (1,6)-Pascal triangle A096956.

6, 55, 280, 1045, 3190, 8437, 20020, 43615, 88660, 170170, 311168, 545870, 923780, 1514870, 2416040, 3759074, 5720330, 8532425, 12498200, 18007275, 25555530, 35767875, 49424700, 67492425, 91158600, 121872036, 161388480, 211822380

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(n) = A096956(n+9, 9) = 6*b(n) - 5*b(n-1) = (n+54)*binomial(n+8, 8)/9, with b(n) = A000582(n+9) = binomial(n+9, 9).

G.f.: (6-5*x)/(1-x)^10.

From Amiram Eldar, Oct 26 2025: (Start)

Sum_{n>=0} 1/a(n) = 3071806649531260786434333432173/16175326304548630032864298248000.

Sum_{n>=0} (-1)^n/a(n) = 55229184*log(2)/296429 - 2086494531709715760110517356639891/16175326304548630032864298248000. (End)

Mathematica

A097300[n_] := (n + 54)*Binomial[n + 8, 8]/9;
Array[A097300, 50, 0] (* Paolo Xausa, May 02 2025 *)

Crossrefs

Cf. A000582, A096956.

Cf. other columns: A096957 (m = 3), A096958 (m = 4), A096959 (m = 5), A097297 (m = 6), A097298 (m = 7), A097299 (m = 8).

Sequence in context: A066514 A281075 A009577 * A295094 A295548 A198855

Adjacent sequences: A097297 A097298 A097299 * A097301 A097302 A097303

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 13 2004

Status

approved