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

0,3

Links

Table of n, a(n) for n=0..18.

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).

Prog

(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));

Crossrefs

Cf. A136630, A381387.

Sequence in context: A041060 A381428 A381177 * A380043 A372251 A381430

Adjacent sequences: A381383 A381384 A381385 * A381387 A381388 A381389

Keyword

nonn

Author

Seiichi Manyama, Feb 22 2025

Status

approved