The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A132228 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A132228

a(n) = Sum_{k=0..n} C(n-1,k)^2*a(k)*a(n-k-1) for n>0 with a(0)=1.
(history; published version)

#6 by Joerg Arndt at Mon May 21 02:33:55 EDT 2018

STATUS

reviewed

approved

#5 by Michael Somos at Sun May 20 16:42:19 EDT 2018

STATUS

proposed

reviewed

#4 by Michael Somos at Sun May 20 16:41:11 EDT 2018

STATUS

editing

proposed

#3 by Michael Somos at Sun May 20 16:40:25 EDT 2018

COMMENTS

Let A(x) = Sum_{n>=0} a(n) * x^n / n!^2. Then A(x)^2 = A'(x) + x * A''(x). - Michael Somos, May 20 2018

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = 1 + O(x); for( k=0, n, A = 1 + intformal( intformal(A^2) / x)); n!^2 * polcoeff(A, n))}; /* Michael Somos, May 20 2018 */

STATUS

approved

editing

Discussion

Sun May 20

16:41

Michael Somos: Added more info.

#2 by Russ Cox at Fri Mar 30 18:37:04 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Aug 15 2007

Discussion

Fri Mar 30

18:37

OEIS Server: https://oeis.org/edit/global/213

#1 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

NAME

a(n) = Sum_{k=0..n} C(n-1,k)^2*a(k)*a(n-k-1) for n>0 with a(0)=1.

DATA

1, 1, 2, 8, 52, 504, 6808, 122304, 2820048, 81183200, 2853990496, 120321094656, 5991955466560, 347996920977664, 23312947041336960, 1784445116557881344, 154767015393810489600, 15098457734490931766784

OFFSET

0,3

PROG

(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, a(k)*a(n-k-1)*binomial(n-1, k)^2 ))

CROSSREFS

Cf. A001059.

KEYWORD

nonn

AUTHOR

Paul D. Hanna (pauldhanna(AT)juno.com), Aug 15 2007

STATUS

approved