The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A349300 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A349300

G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(x)^4)).
(history; published version)

#8 by Michel Marcus at Sun Nov 14 02:25:09 EST 2021

STATUS

editing

proposed

#7 by Michel Marcus at Sun Nov 14 02:25:05 EST 2021

PROG

(PARI) a(n) = sum(k=0, n, (-1)^(n-k) * binomial(n+3*k, 4*k) * binomial(5*k, k) / (4*k+1)); \\ Michel Marcus, Nov 14 2021

STATUS

proposed

editing

#6 by Stefano Spezia at Sun Nov 14 02:21:12 EST 2021

STATUS

editing

proposed

#5 by Stefano Spezia at Sun Nov 14 02:21:00 EST 2021

FORMULA

a(n) = (-1)^5*F([1/5, 2/5, 3/5, 4/5, (1+n)/3, (2+n)/3, (3+n)/3, -n], [1/4, 1/2, 1/2, 3/4, 3/4, 1, 5/4], 3^3*5^5/2^16), where F is the generalized hypergeometric function. - Stefano Spezia, Nov 14 2021

STATUS

proposed

editing

#4 by Ilya Gutkovskiy at Sat Nov 13 17:07:16 EST 2021

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Sat Nov 13 16:38:17 EST 2021

CROSSREFS

Cf. A002294, A005043, A346627, A346665, A349290, A349299, A349301, A349302, A349303.

#2 by Ilya Gutkovskiy at Sat Nov 13 16:27:18 EST 2021

NAME

allocated for Ilya Gutkovskiy

G.f. A(x) satisfies: A(x) = 1 / ((1 + x) * (1 - x * A(x)^4)).

DATA

1, 0, 1, 4, 21, 114, 651, 3844, 23301, 144169, 906866, 5782350, 37289431, 242793439, 1593918916, 10538988984, 70121101825, 469133993094, 3154115695476, 21299373321344, 144402246424591, 982506791975780, 6706724412165956, 45917245477282994

OFFSET

0,4

FORMULA

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n+3*k,4*k) * binomial(5*k,k) / (4*k+1).

MATHEMATICA

nmax = 23; A[_] = 0; Do[A[x_] = 1/((1 + x) (1 - x A[x]^4)) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Table[Sum[(-1)^(n - k) Binomial[n + 3 k, 4 k] Binomial[5 k, k]/(4 k + 1), {k, 0, n}], {n, 0, 23}]

CROSSREFS

Cf. A002294, A005043, A346627, A346665, A349290.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Nov 13 2021

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Sat Nov 13 16:27:18 EST 2021

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved