A097298 Eighth column (m=7) of (1,6)-Pascal triangle A096956.

6, 43, 176, 540, 1380, 3102, 6336, 12012, 21450, 36465, 59488, 93704, 143208, 213180, 310080, 441864, 618222, 850839, 1153680, 1543300, 2039180, 2664090, 3444480, 4410900, 5598450, 7047261, 8803008, 10917456, 13449040, 16463480

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = A096956(n+7, 7) = 6*b(n) - 5*b(n-1) = (n+42)*binomial(n+6, 6)/7, with b(n) = A000580(n+7) = binomial(n+7, 7).

G.f.: (6-5*x)/(1-x)^8.

From Amiram Eldar, Oct 26 2025: (Start)

Sum_{n>=0} 1/a(n) = 2543928665743151131987/12791942966530142812800.

Sum_{n>=0} (-1)^n/a(n) = 689024*log(2)/19721 - 3386900267959349555732207/140711372631831570940800. (End)

Mathematica

A097298[n_] := (n + 42)*Binomial[n + 6, 6]/7;
Array[A097298, 50, 0] (* Paolo Xausa, May 02 2025 *)

Crossrefs

Cf. A000580, A096956.

Cf. other columns: A096957 (m = 3), A096958 (m = 4), A096959 (m = 5), A097297 (m = 6), A097299 (m = 8), A097300 (m = 9).

Sequence in context: A083940 A101071 A299375 * A012872 A156676 A256713

Adjacent sequences: A097295 A097296 A097297 * A097299 A097300 A097301

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 13 2004

Status

approved