The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A372461

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A372461

Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^3) )^(2*n).
(history; published version)

#6 by Michael De Vlieger at Thu May 02 09:46:21 EDT 2024

STATUS

proposed

approved

#5 by Seiichi Manyama at Thu May 02 08:49:41 EDT 2024

STATUS

editing

proposed

#4 by Seiichi Manyama at Wed May 01 22:52:18 EDT 2024

FORMULA

a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(5*n-2*k-1,n-3*k).

CROSSREFS

Cf. A368968, A372465.

#3 by Seiichi Manyama at Wed May 01 22:16:35 EDT 2024

DATA

1, 4, 36, 370, 4012, 44814, 510198, 5886206, 68579020, 805045276, 9507007686, 112817021332, 1344160003030, 16069300956726, 192662610805386, 2315694030560640, 27893938099222316, 336643301659031102, 4069747367955175236, 49274614400855690158

#2 by Seiichi Manyama at Wed May 01 22:14:51 EDT 2024

NAME

allocated for Seiichi ManyamaCoefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^3) )^(2*n).

DATA

1, 4, 36, 370, 4012, 44814, 510198, 5886206, 68579020, 805045276, 9507007686, 112817021332, 1344160003030, 16069300956726, 192662610805386, 2315694030560640

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)^2 * (1-x-x^3)^2 ). See A368968.

PROG

(PARI) a(n, s=3, t=2, u=2) = 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. A368968.

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, May 01 2024

STATUS

approved

editing

#1 by Seiichi Manyama at Wed May 01 22:14:51 EDT 2024

NAME

allocated for Seiichi Manyama

KEYWORD

allocated

STATUS

approved