The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A363575 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A363575

G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + x^k)^3) ).
(history; published version)

#8 by Michael De Vlieger at Sat Jun 10 11:18:30 EDT 2023

STATUS

reviewed

approved

#7 by Joerg Arndt at Sat Jun 10 10:56:00 EDT 2023

STATUS

proposed

reviewed

#6 by Seiichi Manyama at Sat Jun 10 10:04:30 EDT 2023

STATUS

editing

proposed

#5 by Seiichi Manyama at Sat Jun 10 07:39:57 EDT 2023

FORMULA

A(x) = (1 + x)^3 * B(x) where B(x) is the g.f. of A363566.a(n) = Sum_{k=0..3} binomial(3,k) * A363566(n-k).

a(n) = Sum_{k=0..3} binomial(3,k) * A363566(n-k).

PROG

(PARI) seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, subst(A, x, x^k)*x^k/(k*(1+x^k)^3))+x*O(x^n))); Vec(A);

#4 by Seiichi Manyama at Sat Jun 10 07:39:18 EDT 2023

FORMULA

A(x) = (1 + x)^3 * B(x) where B(x) is the g.f. of A363566.a(n) = Sum_{k=0..3} binomial(3,k) * A363566(n-k).

#3 by Seiichi Manyama at Sat Jun 10 07:31:07 EDT 2023

CROSSREFS

Cf. A363548, A363566.

#2 by Seiichi Manyama at Sat Jun 10 07:26:19 EDT 2023

NAME

allocated for Seiichi Manyama

G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + x^k)^3) ).

DATA

1, 1, -1, 1, 2, -4, -1, 10, -3, -20, 19, 38, -70, -65, 221, 73, -640, 117, 1745, -1223, -4433, 5770, 10124, -22007, -18999, 75063, 19307, -235725, 59665, 685744, -525477, -1832544, 2531982, 4364936, -10007555, -8468154, 35302510, 8542655, -114305453

OFFSET

0,5

CROSSREFS

Cf. A198518, A363567.

Cf. A363548.

KEYWORD

allocated

sign

AUTHOR

Seiichi Manyama, Jun 10 2023

STATUS

approved