A158687 Riordan array (1/(1-x),x(1+x)^2/(1-x)).

1, 1, 1, 1, 4, 1, 1, 8, 7, 1, 1, 12, 24, 10, 1, 1, 16, 56, 49, 13, 1, 1, 20, 104, 160, 83, 16, 1, 1, 24, 168, 400, 351, 126, 19, 1, 1, 28, 248, 832, 1120, 656, 178, 22, 1, 1, 32, 344, 1520, 2912, 2561, 1102, 239, 25, 1

Offset

0,5

Comments

Row sums are A077936. Diagonal sums are A129847. Central terms are A059304.

Inverse of alternating signed version is A100326.

Links

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

Formula

Number triangle T(n,k) = Sum_{j=0..n-k} C(n-j,k)*C(2k,j).

T(n,k) = T(n-1,k) + T(n-1,k-1) + 2*T(n-2,k-1) + T(n-3,k-1), T(0,0) = T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Nov 11 2013

G.f.: 1/(1-y-x*(1+y)^2). - Vladimir Kruchinin, Apr 21 2015

Example

Number triangle begins
1,
1, 1,
1, 4, 1,
1, 8, 7, 1,
1, 12, 24, 10, 1,
1, 16, 56, 49, 13, 1,
1, 20, 104, 160, 83, 16, 1

Crossrefs

Cf. A059304, A077936, A100326, A129847.

Sequence in context: A051455 A346875 A289511 * A141541 A334552 A347676

Adjacent sequences: A158684 A158685 A158686 * A158688 A158689 A158690

Keyword

easy,nonn,tabl

Author

Paul Barry, Mar 24 2009

Status

approved