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.

A381140 Expansion of e.g.f. exp( -LambertW(-x * cosh(x)) ).

Original entry on oeis.org

1, 1, 3, 19, 161, 1781, 24667, 409991, 7959233, 176920489, 4432942931, 123648692795, 3800647961761, 127654261471517, 4651982506605995, 182824074836850991, 7708128977570816129, 347059689259637711441, 16621016953663100702755, 843658152872351669816675
Offset: 0

Views

Author

Seiichi Manyama, Feb 15 2025

Keywords

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Crossrefs

Programs

  • PARI
    a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
    a(n) = sum(k=0, n, (k+1)^(k-1)*a185951(n, k));

Formula

E.g.f. A(x) satisfies A(x) = exp( x * cosh(x) * A(x) ).
a(n) = Sum_{k=0..n} (k+1)^(k-1) * A185951(n,k).

A381444 Expansion of e.g.f. ( (1/x) * Series_Reversion( x * exp(-2*x * cosh(x)) ) )^(1/2).

Original entry on oeis.org

1, 1, 5, 52, 837, 18276, 504673, 16871632, 662646281, 29912003344, 1526065495101, 86843677613760, 5454045493422925, 374720831464254016, 27958655248431100313, 2251304544037066606336, 194594761915894781438481, 17971382474574151984603392, 1766073848394482007514748533
Offset: 0

Views

Author

Seiichi Manyama, Feb 23 2025

Keywords

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Crossrefs

Programs

  • PARI
    a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
    a(n) = sum(k=0, n, (2*n+1)^(k-1)*a185951(n, k));

Formula

E.g.f. A(x) satisfies A(x) = exp( x * A(x)^2 * cosh(x * A(x)^2) ).
a(n) = Sum_{k=0..n} (2*n+1)^(k-1) * A185951(n,k).
Showing 1-2 of 2 results.