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

Author

Wolfdieter Lang, Aug 13 2004

Keywords

• nonn
• easy

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).

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).

Programs

Mathematica

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

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.