A265435 - OEIS

A265435

Riordan array (1, x*f(x)) where f(x) is the g.f. of A007564.

1, 0, 1, 0, 1, 1, 0, 4, 2, 1, 0, 19, 9, 3, 1, 0, 100, 46, 15, 4, 1, 0, 562, 254, 82, 22, 5, 1, 0, 3304, 1476, 474, 128, 30, 6, 1, 0, 20071, 8893, 2847, 773, 185, 39, 7, 1, 0, 124996, 55046, 17587, 4796, 1165, 254, 49, 8, 1, 0, 793774, 347922, 111006, 30378, 7461, 1665, 336, 60, 9, 1

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OFFSET

0,8

COMMENTS

Triangle T(n,k), 0<=k<=n, read by rows, given by (0, 1, 3, 1, 3, 1, 3, 1, 3, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

LINKS

Alois P. Heinz, Rows n = 0..140, flattened

EXAMPLE

Triangle begins:

0, 1

0, 1, 1

0, 4, 2, 1

0, 19, 9, 3, 1

0, 100, 46, 15, 4, 1

Production matrix begins:

0, 1

0, 1, 1

0, 3, 1, 1

0, 9, 3, 1, 1

0, 27, 9, 3, 1, 1

0, 81, 27, 9, 3, 1, 1

MATHEMATICA

f[x_]:=(1+2*x-Sqrt[1-8*x+4*x^2])/(6*x); T[n_, k_]:=SeriesCoefficient[(x*f[x])^k, {x, 0, n}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* Stefano Spezia, Feb 05 2025 *)

CROSSREFS

Cf. A007564, A108524 (row sums).

Sequence in context: A110324 A357586 A266861 * A380841 A277004 A371077

Adjacent sequences: A265432 A265433 A265434 * A265436 A265437 A265438

KEYWORD

nonn,tabl,changed

AUTHOR

Philippe Deléham, Dec 09 2015

STATUS

approved