A381346 Expansion of e.g.f. 1/( 1 - sinh(sqrt(2)*x) / sqrt(2) ).

1, 1, 2, 8, 40, 244, 1808, 15632, 154240, 1712656, 21132032, 286800128, 4246266880, 68108302144, 1176458774528, 21772909267712, 429818456473600, 9015349812633856, 200218257664704512, 4693597812326094848, 115820240623410872320, 3000905720793597113344

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 2^k * binomial(n,2*k+1) * a(n-2*k-1).

a(n) = Sum_{k=0..n} k! * 2^((n-k)/2) * A136630(n,k).

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!*2^((n-k)/2)*a136630(n, k));

Crossrefs

Cf. A191277, A381284, A381285, A381286, A381347.

Cf. A136630.

Sequence in context: A376544 A349105 A259869 * A321733 A371313 A000828

Adjacent sequences: A381343 A381344 A381345 * A381347 A381348 A381349

Keyword

nonn

Author

Seiichi Manyama, Feb 20 2025

Status

approved