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Revision History for A257532

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A257532

Triangle, read by rows, T(n,k)=k/n*Sum_{i=0..n-k} C(2*n,n-k-i)*C(2*n+i-1,i).
(history; published version)

#9 by N. J. A. Sloane at Thu Apr 30 21:05:18 EDT 2015

STATUS

editing

approved

#8 by N. J. A. Sloane at Thu Apr 30 21:05:15 EDT 2015

CROSSREFS

Cf. A027307. First column = A032349.

STATUS

proposed

editing

#7 by Michel Marcus at Thu Apr 30 15:43:20 EDT 2015

STATUS

editing

proposed

#6 by Michel Marcus at Thu Apr 30 15:41:53 EDT 2015

FORMULA

G.f.: 1/(1-x*B(x)^2*y)-1, where B(x) is g.f. of A027307.

CROSSREFS

Cf. A027307.

STATUS

proposed

editing

Discussion

Thu Apr 30

15:43

Michel Marcus: 1st column : A032349  ?

#5 by Vladimir Kruchinin at Tue Apr 28 11:21:22 EDT 2015

STATUS

editing

proposed

#4 by Vladimir Kruchinin at Tue Apr 28 11:20:50 EDT 2015

FORMULA

G.f.: 1/(1-x*AB(x)^2*y)-1, where AB(x) is g.f. of A027307.

G.f. satisfies A(x)=x*[(1+A(x))/(1-A(x))]^2.

#3 by Vladimir Kruchinin at Tue Apr 28 11:17:09 EDT 2015

DATA

1, 4, 1, 24, 8, 1, 172, 64, 12, 1, 1360, 536, 120, 16, 1, 11444, 4672, 1156, 192, 20, 1, 100520, 42024, 11088, 2096, 280, 24, 1, 911068, 387456, 106908, 22016, 3420, 384, 28, 1, 8457504, 3643448, 1038984, 227408, 39120, 5192, 504, 32, 1, 80006116, 34814848, 10182036, 2332608, 432004, 64320, 7476, 640, 36, 1

FORMULA

G.f.: 1/(1-x*A(x)^2*y), -1, where A(x) is g.f. of A027307

EXAMPLE

1;

4, 1;

24, 8, 1;

172, 64, 12, 1;

1360, 536, 120, 16, 1;

#2 by Vladimir Kruchinin at Tue Apr 28 11:13:58 EDT 2015

NAME

allocated for Vladimir Kruchinin

Triangle, read by rows, T(n,k)=k/n*Sum_{i=0..n-k} C(2*n,n-k-i)*C(2*n+i-1,i).

DATA

OFFSET

1,2

FORMULA

G.f.: 1/(1-x*A(x)^2*y), where A(x) is g.f. of A027307

PROG

(Maxima)

T(n, k):=(k*sum(binomial(2*n, n-k-i)*binomial(2*n+i-1, i), i, 0, n-k))/n;

CROSSREFS

Cf. A027307

KEYWORD

allocated

nonn,tabl

AUTHOR

Vladimir Kruchinin, Apr 28 2015

STATUS

approved

editing

#1 by Vladimir Kruchinin at Tue Apr 28 11:13:58 EDT 2015

NAME

allocated for Vladimir Kruchinin

KEYWORD

allocated

STATUS

approved