A381386 E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)^2) ).

1, 1, 6, 73, 1360, 34321, 1095584, 42350673, 1923628032, 100430070721, 5926517800192, 390116250605401, 28341322114027520, 2252512575040254801, 194421212092585943040, 18110799663166635386017, 1810994441189833169698816, 193488658627430346315888385, 21997611392941496027173879808

Offset: 0

Author

Seiichi Manyama, Feb 22 2025

Keywords

• nonn

Crossrefs

Cf. A136630, A381387.

Programs

PARI

a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, k!*binomial(2*n+k+1, k)/(2*n+k+1)*a136630(n, k));

Formula

a(n) = Sum_{k=0..n} k! * binomial(2*n+k+1,k)/(2*n+k+1) * A136630(n,k).

E.g.f.: ( (1/x) * Series_Reversion( x*(1 - sinh(x))^2 ) )^(1/2).