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A111106 Riordan array (1, x*g(x)) where g(x) is g.f. of double factorials A001147. 4
1, 0, 1, 0, 1, 1, 0, 3, 2, 1, 0, 15, 7, 3, 1, 0, 105, 36, 12, 4, 1, 0, 945, 249, 64, 18, 5, 1, 0, 10395, 2190, 441, 100, 25, 6, 1, 0, 135135, 23535, 3807, 691, 145, 33, 7, 1, 0, 2027025, 299880, 40032, 5880, 1010, 200, 42, 8, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Triangle T(n,k), 0 <= k <= n, given by [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...] DELTA [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

T(n, k) = Sum_{j=0..n-k} T(n-1, k-1+j)*A111088(j).

Sum_{k=0..n} T(n, k) = A112934(n).

G.f.: 1/(1-xy/(1-x/(1-2x/(1-3x/(1-4x/(1-... (continued fraction). - Paul Barry, Jan 29 2009

Sum_{k=0..n} T(n,k)*2^(n-k) = A168441(n). - Philippe Deléham, Nov 28 2009

EXAMPLE

Rows begin:

  1;

  0,       1;

  0,       1,      1;

  0,       3,      2,     1;

  0,      15,      7,     3,    1;

  0,     105,     36,    12,    4,    1;

  0,     945,    249,    64,   18,    5,   1;

  0,   10395,   2190,   441,  100,   25,   6,  1:

  0,  135135,  23535,  3807,  691,  145,  33,  7, 1;

  0, 2027025, 299880, 40032, 5880, 1010, 200, 42, 8, 1;

CROSSREFS

Columns: A000007, A001147, A034430; diagonals: A000012, A001477, A055998.

Cf. A084938, A111088, A112934, A168441.

Sequence in context: A085771 A253286 A284799 * A321964 A197819 A232006

Adjacent sequences:  A111103 A111104 A111105 * A111107 A111108 A111109

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Oct 13 2005, Dec 20 2008

STATUS

approved

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Last modified March 8 20:14 EST 2021. Contains 341953 sequences. (Running on oeis4.)