The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A372458

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A372458

Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^2)^2 )^n.
(history; published version)

#7 by Michael De Vlieger at Thu May 02 09:46:28 EDT 2024

STATUS

proposed

approved

#6 by Seiichi Manyama at Thu May 02 08:46:27 EDT 2024

STATUS

editing

proposed

#5 by Seiichi Manyama at Thu May 02 08:21:47 EDT 2024

CROSSREFS

Cf. A368965, A372233.

#4 by Seiichi Manyama at Thu May 02 08:11:18 EDT 2024

FORMULA

a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k-1,k) * binomial(4*n-k-1,n-2*k).

#3 by Seiichi Manyama at Wed May 01 22:07:19 EDT 2024

DATA

1, 3, 25, 225, 2129, 20723, 205471, 2063890, 20931585, 213864939, 2198044805, 22699471171, 235354244255, 2448409104820, 25544033624414, 267158874185420, 2800191197529633, 29405702263792875, 309320021637262225, 3258658594126096867, 34376186445159365709

#2 by Seiichi Manyama at Wed May 01 22:06:16 EDT 2024

NAME

allocated for Seiichi ManyamaCoefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^2)^2 )^n.

DATA

1, 3, 25, 225, 2129, 20723, 205471, 2063890, 20931585, 213864939, 2198044805, 22699471171, 235354244255, 2448409104820, 25544033624414, 267158874185420

OFFSET

0,2

FORMULA

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x) * (1-x-x^2)^2 ). See A368965.

PROG

(PARI) a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t+u+1)*n-(s-1)*k-1, n-s*k));

CROSSREFS

Cf. A368965.

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, May 01 2024

STATUS

approved

editing

#1 by Seiichi Manyama at Wed May 01 22:06:16 EDT 2024

NAME

allocated for Seiichi Manyama

KEYWORD

allocated

STATUS

approved