cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A117377 Riordan array (1-4x,x(1-x)).

Original entry on oeis.org

1, -4, 1, 0, -5, 1, 0, 4, -6, 1, 0, 0, 9, -7, 1, 0, 0, -4, 15, -8, 1, 0, 0, 0, -13, 22, -9, 1, 0, 0, 0, 4, -28, 30, -10, 1, 0, 0, 0, 0, 17, -50, 39, -11, 1, 0, 0, 0, 0, -4, 45, -80, 49, -12, 1, 0, 0, 0, 0, 0, -21, 95, -119, 60, -13, 1
Offset: 0

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Author

Paul Barry, Mar 10 2006

Keywords

Comments

Row sums are A117378. Diagonal sums are A117379. Inverse is A117380.

Examples

			Triangle begins
1,
-4, 1,
0, -5, 1,
0, 4, -6, 1,
0, 0, 9, -7, 1,
0, 0, -4, 15, -8, 1,
0, 0, 0, -13, 22, -9, 1,
0, 0, 0, 4, -28, 30, -10, 1

Formula

Number triangle T(n,k)=(-1)^(n-k)(C(k,n-k)+4*C(k, n-k-1))

A117381 Expansion of 1/((1-4*x*c(x))(1-x^2*c(x))), c(x) the g.f. of A000108.

Original entry on oeis.org

1, 4, 21, 109, 575, 3047, 16192, 86171, 458972, 2445825, 13037508, 69509558, 370634265, 1976421031, 10539858413, 56208784808, 299766435277, 1598704176149, 8526238418811, 45472594256564, 242517996824355
Offset: 0

Views

Author

Paul Barry, Mar 10 2006

Keywords

Comments

Diagonal sums of number triangle A117380.

Formula

a(n)=sum{k=0..floor(n/2), [k<=n-k]*sum{j=0..n-k, (j/(n-k-j))*C(2n-k-j,n-k-j)[k<=j]*4^(j-k)}}
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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