cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A379257 G.f. A(x) satisfies A(x) = 1 + x * A(x)^3 * (1 + A(x)^7).

Original entry on oeis.org

1, 2, 26, 530, 12850, 342370, 9684010, 285483666, 8675363298, 269823659586, 8547536496442, 274825739078930, 8945617644054546, 294204116545534370, 9761360051405903434, 326339380099797219474, 10982521821776648986050, 371758494418806559639170
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2024

Keywords

Crossrefs

Cf. A379256.

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(n, k)*binomial(3*n+7*k+1, n)/(3*n+7*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * binomial(3*n+7*k+1,n)/(3*n+7*k+1).

A379254 G.f. A(x) satisfies A(x) = ( (1 + x*A(x))/(1 - x*A(x)^2) )^3.

Original entry on oeis.org

1, 6, 72, 1136, 20496, 400176, 8230592, 175643712, 3852905472, 86338960640, 1967950718976, 45483461999616, 1063433350498304, 25107661327202304, 597766180153565184, 14335020154675867648, 345948883288769740800, 8395511682729703931904
Offset: 0

Views

Author

Seiichi Manyama, Dec 19 2024

Keywords

Crossrefs

Cf. A213282, A365843, A379255.
Cf. A379256.

Programs

  • PARI
    a(n) = sum(k=0, n, binomial(3*n+4*k+2, k)*binomial(3*n+3*k+3, n-k)/(n+k+1));

Formula

G.f.: B(x)^3 where B(x) is the g.f. of A379256.
a(n) = Sum_{k=0..n} binomial(3*n+4*k+2,k) * binomial(3*n+3*k+3,n-k)/(n+k+1).
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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