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.

A381745 Expansion of exp( Sum_{k>=1} binomial(8*k-1,2*k) * x^k/k ).

Original entry on oeis.org

1, 21, 903, 49525, 3070308, 204928371, 14369906538, 1043861319189, 77866470852108, 5929621690613108, 459076176165983247, 36026517938705145267, 2859318461620989381900, 229114879928544260792946, 18509862380800289696106372, 1506048000721264678984095445, 123303480420582227597300406588
Offset: 0

Views

Author

Seiichi Manyama, Mar 05 2025

Keywords

Links

Crossrefs

Cf. A079489, A381744, A381746.
Cf. A006632, A381751.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, binomial(8*k-1, 2*k)*x^k/k)))

Formula

G.f. A(x) satisfies A(x^2) = B(x)/x * B(-x)/(-x), where B(x) is the g.f. of A006632.
a(n) = Sum_{k=0..2*n} (-1)^k * A006632(k+1) * A006632(2*n-k+1).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(8*k-1,2*k) * a(n-k).
G.f.: B(x)^3, where B(x) is the g.f. of A381751.

A381746 Expansion of exp( Sum_{k>=1} binomial(10*k-1,2*k) * x^k/k ).

Original entry on oeis.org

1, 36, 2586, 235884, 24284907, 2689924444, 312907382800, 37699275223260, 4663450108073401, 588854988193808392, 75589352418472567340, 9834912295258236849604, 1294095251234713917535805, 171909332777340128148714400, 23024035140764003881788203616
Offset: 0

Views

Author

Seiichi Manyama, Mar 05 2025

Keywords

Links

Crossrefs

Cf. A079489, A381744, A381745.
Cf. A118971, A381752.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, binomial(10*k-1, 2*k)*x^k/k)))

Formula

G.f. A(x) satisfies A(x^2) = B(x) * B(-x), where B(x) is the g.f. of A118971.
a(n) = Sum_{k=0..2*n} (-1)^k * A118971(k) * A118971(2*n-k).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(10*k-1,2*k) * a(n-k).
G.f.: B(x)^4, where B(x) is the g.f. of A381752.
Showing 1-2 of 2 results.

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

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