The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A111959 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A111959

Renewal array for aerated central binomial coefficients.
(history; published version)

#29 by Joerg Arndt at Tue Aug 31 02:56:38 EDT 2021

STATUS

reviewed

approved

#28 by Sean A. Irvine at Mon Aug 30 22:50:30 EDT 2021

STATUS

proposed

reviewed

#27 by Jon E. Schoenfield at Wed Aug 18 20:18:55 EDT 2021

STATUS

editing

proposed

#26 by Jon E. Schoenfield at Wed Aug 18 20:18:51 EDT 2021

FORMULA

G.f.: 1/(1-xy-2x^2/(1-x^2/(1-x^2/(1-x^2/(1-.... (continued fraction). [_- _Paul Barry_, Jan 28 2009]

STATUS

proposed

editing

#25 by Jon E. Schoenfield at Tue Aug 17 01:05:11 EDT 2021

STATUS

editing

proposed

#24 by Jon E. Schoenfield at Tue Aug 17 01:05:10 EDT 2021

EXAMPLE

0, 1;

2, 0, 1;

0, 4, 0, 1;

6, 0, 6, 0, 1;

0, 16, 0, 8, 0, 1;

0, 0;

2, 0, 0;

0, 4, 0, 0;

0, 0, 6, 0, 0;

0, 0, 0, 8, 0, 0; (End)

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proposed

editing

#23 by Michel Marcus at Tue Aug 17 00:16:45 EDT 2021

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editing

proposed

#22 by Michel Marcus at Tue Aug 17 00:16:41 EDT 2021

COMMENTS

Row sums are A098615.

Binomial transform (product with C(n,k)) is A111960.

Diagonal sums are A026671 (with interpolated zeros).

Row sums are A098615. Binomial transform (product with C(n,k)) is A111960. Diagonal sums are A026671 (with interpolated zeros). Inverse is (1/sqrt(1+4x^2),x/sqrt(1+4x^2)), or (sqrt(-1))^(n-k)*T(n,k); . [corrected by Peter Bala, Aug 13 2021.]

STATUS

proposed

editing

#21 by Jon E. Schoenfield at Mon Aug 16 20:29:12 EDT 2021

STATUS

editing

proposed

#20 by Jon E. Schoenfield at Mon Aug 16 20:29:09 EDT 2021

COMMENTS

FORMULA

Riordan array (1/sqrt(1-4x^2), x/sqrt(1-4x^2)); Number number triangle T(n, k)=(1+(-1)^(n-k))*binomial((n-1)/2, (n-k)/2)*2^(n-k)/2.

STATUS

proposed

editing