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A201165 Triangle read by rows: Pascal's triangle (A007318) times the Fibonacci triangle (A139375). 2
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 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Apr 03 2020 *)

CROSSREFS

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

Sequence in context: A201166 A318942 A188137 * A171488 A171651 A104710

Adjacent sequences:  A201162 A201163 A201164 * A201166 A201167 A201168

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Nov 27 2011

STATUS

approved

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Last modified September 22 03:20 EDT 2021. Contains 347605 sequences. (Running on oeis4.)