A201165 Triangle read by rows: Pascal's triangle (A007318) times the Fibonacci triangle (A139375).

1, 2, 1, 5, 4, 1, 13, 14, 6, 1, 34, 48, 27, 8, 1, 89, 166, 111, 44, 10, 1, 233, 587, 443, 210, 65, 12, 1, 610, 2138, 1761, 941, 353, 90, 14, 1, 1597, 8046, 7059, 4101, 1752, 548, 119, 16, 1, 4181, 31285, 28701, 17697, 8289, 2984, 803, 152, 18, 1, 10946, 125396, 118631, 76342, 38233, 15231, 4761, 1126, 189, 20, 1

Offset

0,2

Links

Table of n, a(n) for n=0..65.

Tian-Xiao He and Renzo Sprugnoli, Sequence characterization of Riordan arrays, Discrete Math. 309 (2009), no. 12, 3962-3974.

Formula

T(n,k) = Sum_{j=k..n} A007318(n,j)*A139375(j,k).

Example

Triangle begins:
1
2 1
5 4 1
13 14 6 1
34 48 27 8 1
89 166 111 44 10 1
233 587 443 210 65 12 1
...

Maple

A201165 := proc(n, k)
    add( binomial(n, j)*A139375(j, k), j=k..n) ;
end proc: # R. J. Mathar, Jul 09 2013

Mathematica

F[n_, k_] := If[k == 0, Fibonacci[n+1], k Sum[Fibonacci[i+1] Binomial[2(n-i)-k-1, n-i-1]/(n-i), {i, 0, n-k}]];
T[n_, k_] := Sum[Binomial[n, j] F[j, k], {j, k, n}];
Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 03 2020 *)

Crossrefs

Cf. A007318, A139375, A201166, A001519 (1st column).

Sequence in context: A201166 A318942 A188137 * A171488 A171651 A348451

Adjacent sequences: A201162 A201163 A201164 * A201166 A201167 A201168

Keyword

nonn,tabl

Author

N. J. A. Sloane, Nov 27 2011

Status

approved